text:
Foster the People is een Amerikaanse indierockband, die in 2009 werd opgericht te Los Angeles.

Geschiedenis

–2010: ontstaan van de band
Mark Foster is geboren in Californië maar groeide op in Ohio. Hij was twee jaar oud toen hij muziek maken leuk begon te vinden en als tiener heeft hij in een metalband gespeeld. Foster wilde eigenlijk fotograaf of computerprogrammeur worden en heeft nooit zo nagedacht over een carrière als muzikant. Na de middelbare school heeft hij toch zeven jaar als soloartiest gewerkt en af en toe nummers gemaakt voor verschillende reclames. Omdat Foster niet genoeg verdiende met zijn muziek had hij een bijbaantje in een restaurant en als pizzabezorger.

Na zeven jaar richtte hij een band op omdat Foster in zijn nummers veel meer instrumenten begon te gebruiken en hij andere muzikanten nodig had om die te bespelen. Het was volgens Foster moeilijk om de juiste personen te vinden, maar toen hij samen met Mark Pontius en Cubbie Fink begon te spelen klikte het meteen.

Foster ontmoette Fink op een 'pokeravond' en Mark Pontius leerde hij via een gezamenlijke vriend kennen. Fink komt oorspronkelijk uit San Diego. In oktober 2009 speelde de band voor het eerst samen. Foster moest stoppen met zijn bijbaantjes en leefde toen van de muziek die hij met zijn vrienden maakte. Zach "Reazon" Heiligman zat eerder ook bij de band, maar heeft nu alleen nog een rol achter de schermen. Hij is een erg goede vriend van Foster. Ze hebben samen aan een hiphopproject gewerkt vlak voor en tijdens het ontstaan van de band. Omdat de liedjes van Foster the People zoveel instrumenten bevatten, toeren er nog twee andere muzikanten mee: Sean Cimono (gitaar, keyboard en achtergrondzang) en Isom Innis (keyboard en piano). Cimono staat vermeld op het album Torches met het nummer 'Waste'. Over Innis wordt niet gesproken, waarschijnlijk omdat hij niet of onvoldoende heeft meegeholpen met het album.

2010–2012: Torches
De band begon met nummers in de studio opnemen in 2010. Begin 2011 bracht de band de ep Foster the People uit, met de nummers "Houdini", "Pumped Up Kicks" en "Helena Beat". Hun eerste en tot nu toe grootste hit was "Pumped Up Kicks" van deze ep. Het gaat over een buitenbeentje dat zijn verstand begint te verliezen en wraak wil nemen op mensen. Foster heeft er een vrolijk liedje van gemaakt ondanks de tekst omdat het volgens hem anders een deprimerend nummer werd. Hij heeft het nummer in ongeveer twee dagen geschreven, dat oorspronkelijk voor een advertentie bedoeld was. Terwijl het nummer een sleeper hit werd, eerst vaak gespeeld op modern/alternatieve rockradiostations, vervolgens "crossed over" naar hitradio, bracht de band zijn debuutalbum Torches uit, op 23 mei 2011. Het telt 10 tracks, waarvan zeven nieuwe en drie van de ep. Een versie met drie extra nummers en een aantal remixen werd gelimiteerd op tournee verkocht. Ook werden de singles "Helena Beat", "Call It What You Want" en "Don't Stop (Color on the Walls)" uitgebracht, alsmede de promo-single "Houdini", die allemaal goed scoorden.

2012–2014: Supermodel
Hoewel de bandleden weinig tijd hadden tijdens hun tour, werkten ze toch aan nieuw materiaal. Meer naar het einde van de tournees begonnen ze een aantal nieuwe nummers te spelen: "Surfing" (Pseudologia Fantastica), "Level Up" (A Beginner's Guide to Destroying the Moon) en "Coming of Age". In interviews stelde Mark Foster dat het album "niet het tweede album zou zijn dat men [van ons] zou verwachten".

Een teaser werd op nieuwjaarsdag 2014 geüpload naar het YouTube-kanaal van de band, met een stuk van "Coming of Age" op de achtergrond. Op 13 januari werd Supermodel officieel aangekondigd, en op 14 januari kwam de eerste single uit, die ook "Coming of Age" was. Twee singles volgden, "Pseudologia Fantastica" en "Best Friend", terwijl het album erg werd gepromoot. Het album werd op 18 maart uitgebracht, maar was op 14 maart al op Spotify te beluisteren en iets daarvoor al op het internet uitgelekt. Op het conceptalbum focust de band meer op alternatieve rock, met een stuk minder elektronische invloeden en enkel echte instrumenten gebruikt, vooral met veel meer gitaren. Het kreeg gemengde reviews, vooral van wie een Torches deel twee had verwacht.

Op 15 april werd, ook op Spotify, een live-ep opgenomen in The Village uitgebracht, met de nummers "Best Friend", "A Beginner's Guide to Destroying the Moon", "Coming of Age", "Pseudologia Fantastica" en "The Truth" van Supermodel.

2017: Sacred Hearts Club
In 2017 bracht de band het derde studioalbum Sacred Hearts Club op de markt. Deze was wereldwijd minder succesvol dan haar twee voorgangers. De van het album afkomstige single Sit next to me werd wel een grote hit in de Alternative Songs-hitlijst.

Bezetting
 Mark Foster - zang, keyboard, gitaar, percussie.
 Mark Pontius (bijnaam: Ponsi) - percussie.
 Cubbie Fink (echte naam: Jacob) - basgitaar, achtergrondzang.

Discografie

Albums

|-
|align="left"|Foster the People (EP)||2010||-|||||| ep
|-
|align="left"|Torches||24-06-2011||02-07-2011||53||17||
|-
|align="left"|Supermodel||14-03-2014||22-03-2014||57||1||
|-
|align="left"|Sacred Hearts Club||21-07-2017||29-07-2017||85||1||
|}

|-
|align="left"|Torches||2011||02-07-2011||69||9||
|-
|align="left"|Supermodel||2014||22-03-2014||93||3||
|}

Singles

|-
|align="left"|Pumped up kicks||04-04-2011||09-07-2011||34||5|| Nr. 35 in de Single Top 100
|-
|align="left"|Houdini||2011||20-08-2011||tip10||-|| Nr. 98 in de Single Top 100
|-
|align="left"|Call it what you want||07-11-2011||07-01-2012||tip3||-||
|}

|-
|align="left"|Pumped up kicks||2011||04-06-2011||30||6||
|-
|align="left"|Call it what you want||2011||26-11-2011||tip16||-||
|}

Radio 2 Top 2000

Amerikaanse rockband
Indiegroep
Cultuur in Los Angeles

redpajama_set_name: RedPajamaWikipedia


text:
University of Toronto Colloquium in Medieval Philosophy 2017
Chair: Charles Brittain (University of Toronto)
Speaker: Jorge Gracia (SUNY Buffalo): "Individuation and the Realism/Nominalism Dilemma: The Case of the Middle Ages"
Commentator: Richard Cross (University of Notre Dame)
Chair: Jeannie Miller (University of Toronto)
Speaker: Richard Taylor (Marquette University): "Averroes on the Attainment of Happiness"
Commentator: Stephen Ogden (The Catholic University of America)
Chair: Simona Vucu (University of Toronto)
Nicholas Oschman (Marquette University): "Two Philosophical Critiques of Prophecy: Abū Bakr al-Rāzī and Abū Naṣr al-Fārābī on the Pre-Eminence of Natural Reason"
Francesco Pica (University of Toronto): "Getting at Reality: John Duns Scotus on Mind and the World"
Deni Gamboa (UNAM Mexico City): "William of Ockham on Introspective Cognition of Intuitive Acts' Content and Likeness"
Chair: Stephen Dumont (University of Notre Dame)
Thomas Williams (University of South Florida): "Can Anselm Have Everything He Wants?"
Commentator: Giorgio Pini (Fordham University)
All sessions will be held in the Jackman Humanities Building (170 St. George St.), Room 100.
All sessions are free and open to the public.
Registration and inquiries: medieval.philosophy@utoronto.ca.
Organizers: Deborah Black, Peter King, Martin Pickave

redpajama_set_name: RedPajamaCommonCrawl


text:
Der Allgemeine Deutsche Schriftverein wurde 1890 von Adolf Reinecke im Rahmen des Antiqua-Fraktur-Streits als Gegenverein zum Verein für Altschrift gegründet. Der Verein trat für die Reinhaltung der deutschen Sprache und Schrift und insbesondere für die Stärkung der Frakturschrift ein und wandte sich scharf gegen die Verwendung der Antiqua-Schrift. Publikationsorgan des Vereins war die Zeitschrift Heimdall. Zeitschrift für reines Deutschtum und All-Deutschtum.

Vereinsgeschichte
Reinecke war nicht nur Gründer des Allgemeinen Deutschen Schriftvereins, dessen zweiter Vorsitzender und Herausgeber des Vereinsorgans Heimdall. Er war zudem auch Gründer und Vorsitzender des Berliner Zweigs des Allgemeinen Deutschen Sprachvereins. Im Rahmen des Antiqua-Fraktur-Streits kam es zu Auseinandersetzungen zwischen dem Berliner Zweig und dem Gesamtverein, den Reinecke immer wieder scharf angriff, weil sich der Gesamtverein nicht für die Verwendung der Frakturschrift einsetzen wollte, sondern die Diskussion um die deutsche Schrift in seiner Satzung als Vereinsziel gar explizit ausgeschlossen hatte. Zugleich kritisierte der Gesamtverein den Namen von Reineckes kleinem und eher unbedeutendem Allgemeinen Deutschen Schriftverein, der in Pressemeldungen zum Antiqua-Fraktur-Streit immer wieder mit dem großen und einflussreichen Allgemeinen Deutschen Sprachverein verwechselt wurde. All dies führte schließlich zum zwangsweisen Ausschluss des Berliner Zweigs aus dem Gesamtverein. Daraufhin gründete Reinecke 1898 den Alldeutschen Sprach- und Schriftverein, in dem sowohl der von ihm gegründete Berliner Sprachverein als auch sein Allgemeiner Deutscher Schriftverein aufging.

Politische Ausrichtung
Der Verein war Mitglied in dem rechtsgerichteten Dachverband der Vereinigten Vaterländischen Verbände Deutschlands. Zudem war der Verein antisemitisch ausgerichtet.

Siehe auch
 Liste deutscher Sprachvereine

Wissenschaftliche Literatur
 Willi Buch [Pseudonym für: Wilhelm Buchow]: 50 Jahre antisemitische Bewegung. Beiträge zu ihrer Geschichte. Deutscher Volksverlag, München 1937.
 Dieter Fricke: Die bürgerlichen Parteien in Deutschland. Handbuch der Geschichte der bürgerlichen Parteien und anderer bürgerlicher Interessenorganisationen vom Vormärz bis zum Jahre 1945. Band 2, Fraktion Augsburger Hof – Zentrum. DEB Verlag das europäische Buch, Berlin 1974.
 Silvia Hartmann: Fraktur oder Antiqua. Der Schriftstreit von 1881 bis 1941 (= Theorie und Vermittlung der Sprache, 28). Lang, Frankfurt am Main / New York 1998.
 Johannes Müller: Die Wissenschaftlichen Vereine und Gesellschaften Deutschlands im neunzehnten Jahrhundert. Bibliographie ihrer Veröffentlichungen. Zweiter Band (fortgeführt bis 1914), erste Hälfte: Aachen – Frankfurt a. M. Behrend & Co, Berlin 1917.

Einzelnachweise

Organisation (Schreiben)
Organisation (deutsche Sprache)
Gegründet 1890
Aufgelöst 1898


Southwest Community Campus [SWCC] is located on the Southwest side of Grand Rapids in a historic school building. The school has had modern updates, including a new cafeteria, while maintaining its historic charm. This unique school offers a proven dual immersion experience in English and Spanish to help students become bilingual and bicultural.
Mentoring typically occurs over lunch [between 11am-1pm].
Have questions about mentoring at this school? Contact the SWCC Site Coordinator at swcc@affinitymentoring.org or 616.819.6799.


text:
Panametrics Leases 11,000 SF At Minolta
HOUSTON-The Massachusetts-based high-tech firm commits to flex/warehouse space in a building in the northwest Houston "Big Box" area that is 52% occupied.
By Jennifer Brenner Andrade | December 13, 2001 at 01:01 AM
HOUSTON-Panametrics, Inc., a Massachusetts-based high technology firm that specializes in research and development in the physical sciences, with particular expertise in the area of acoustics, chemistry, and radiation physics, has leased 10,891 sf of industrial space at the Minolta Building at 7255 Langtry #100 in Houston. The building is located between Texas 290 and Hollister in the Big Box area of town.
Keith Lloyd with the Houston office of Grubb & Ellis Co. represented Panametrics. Mike Annino with InSite Realty represented the landlord, NWP/InSite GP, LLC. Panametrics has its Houston offices at 820 Gessner.
The Minolta Building, a 20,877 sf, one story building in northwest Houston, is 52% leased and has a clear height of 12 feet. The building is considered a flex/warehouse structure.


Anyone got any ideas on how to do a really great m-learning module that doesn't cost too much to develop?
Hi RogerD, m-learning modules are relatively cheap to develop compared to traditional e-learning courses. We develop m-learning modules for our clients using captivate and storyline. What do you want to do with the m-learning modules? Do you already have content that can be adapted like videos that can be edited?
Developing a mobile learning module involves great effort in the form of design, development, testing and deployment instead you could go with the best mobile learning platform in the market such as 'Instancy Mobile Learning Platform' that servers many advanced module needs.


text:
We Take A Look Inside The Twisted Mind Of R Kelly
By Joe Tinkler
With R Kelly dropping his eleventh studio album this month, we take a retrospective look at the crazy of his most successful hit: Ignition (Remix).
I believe that it is the duty of the unemployed or those with a lot of spare time on their hands to delve into important matters. Matters that those in full time work have pondered but never really gotten a full grasp on. Well, today I am going to be that guy and today's topic of discussion you ask? An investigation in to the lyrics of R Kelly's superb hit Ignition (Remix).
Now all I know is that the track was released in 2003 (a great year for us all I'm sure) and became the most successful single of the noughties. I have fond memories of the exact moment the song dropped in the UK. It felt revolutionary. It was the catchiest song of all time. Even the school grebs (me) couldn't resist its pull. It was only knocked off the top spot by Goth Metal behemoth Evanescence with their atrocious contribution to rap-metal via 'Bring me to Life'. Admittedly, when I first heard BMTL I actually thought it was a treat, which leads me to ask, did people lose their minds during the first part of the 21st century or something? SERIOUSLY, WHAT WERE WE THINKING?
Anyway, as per, I'm wandered away from the point. What I am trying to say is, even though Ignition was a certified banger of a song, (a song so banging that at most parties it's used in times of emergency, like when the ladies are starting to depart the dancefloor because some douche thinks it's cool to put a random Krautrock song on that only he and his loser mates know. Goddamn I hate you Tom Owen) no one has really made any probing inquiries in to just how whackjob the lyrics actually are. Sure, you can snigger and be like "nah but Same Girl is the real crazy one". Well yeah, but Ignition still has its moments. Let's crack on.
No I'm not tryin' to be rude,
But hey pretty girl I'm feelin' you
The way you do the things you do
Remind me of my Lexus Coupe
Right, the first two lines are absolutely fine; a great little gambit to initiate conversation with the opposite sex. Who doesn't wanna be told by the dude that wrote the Space Jam theme that you're fly? However, following that up by a comparing her to a Lexis Coupe, are you mad? You're really gonna base the whole of your serenade around car metaphors? Really dude? REALLY?
Look, this is the 2003 Lexus Coupe. It's not even that sexy of a car. It's bulky and a bit angular. Why not a curvy Fiat Punto? A Small, sexy and elegant car. Oh well.
You must be a football coach
The way you got me playin' the field
Hmm, this isn't as bad but the imagery that I conjure up in my mind of a football coach is the stereotypical middle-aged 'wanted-to-go-pro-but-was-sidelined-by-a-knee-injury-so-now-I'm-fat-and-bald-and-angry' type of guy. This would not sit well for me if I was the said lady but I guess he brings it back by telling her that her sports instructor-like aura is making him want to have sex with loads of other women. "Damn girl, you're so fine that I wanna be a player forever". Sexy AND romantic.
☛ Read Next: Reporter Almost Dies By Getting Hit By A Baseball When Taking The Most Dangerous Selfie Ever
Related Items:2003, Ignition, Ignition (remix), R. Kelly, RnB
One Of R. Kelly's Alleged Victims Says That They're Now Engaged
Court Documents Show A Mum Coached Her 17-Year-Old Daughter On How To Seduce R Kelly
Beyoncé Is Running #MeToo Checks On Collaborators For New 'Renaissance' Album
Best New Tumblr Find: Nicolas Cage Cats
Sick Chirpse Featured Artist #3: El Tacodor


text:
Tepetitlán, även San Antonio Tepetitlán, är en ort i Mexiko, tillhörande kommunen Chiautla i delstaten Mexiko. Tepetitlán ligger i den centrala delen av landet och tillhör Mexico Citys storstadsområde. Orten hade 2 377 invånare vid folkräkningen 2010, och är kommunens fjärde största ort sett till befolkning.

Referenser

Orter i Chiautla, Mexiko


Cute Above Kitchen Cupboard Lighting 35 For Your Interior Home Inspiration with Above Kitchen Cupboard Lighting is free HD wallpaper. This wallpaper was upload at March 19, 2018 upload by amri in .
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It's Saturday and time to review the treats from the week. SYTYCD was back in a Mia Michaels kind of way. I've picked a powerful performance for you and you're not going to want to miss it.
Jami Gold : Michael Hauge's Workshop: Are These Characters the Perfect Match?
Liz Bureman at The Write Practice : Do You Use Quotation Marks or Italics for Song and Album Titles?
This week the great dance show was back and all performances were choreographed by Mia Michaels. Oh, bells!! Love Mia's choreography. But the Top-14 faced a great dancer-challenge. They'd be performing previously performed routines, routines choreographed for past seasons, making it really easy to see where this year's dancers fall short in direct comparison to past contestants. It may have been a bit cruel, but so is the life of a dancer. One performance stood out. It was not better than the original, but stood on its own. This routine made me cry when Kayla and Kupono performed it in season five, so powerful. I do suggest watching both performances, but please watch Lindsay and Cole first.
Both performances made me cry, how about you?
Thanks for another fabulous week bloggers. I keep learning from you each week and I appreciate all that you do. Hubs is back this week with his second pick (see his 1st pick in last weeks post) in his snazzy theme: Really great drummers who are also really great singer/songwriter/guitarists.
Jami Gold : Blogiversary Winners & a Gift for All <–with a must see downloadable spreadsheet!
"Her Song" by Brian Blade, from the album "Mama Rosa".
You should also look for the song "After the Revival" I couldn't find a video link for that one, but it's my favorite song on that record.
Brian Blade is one of my favorite drummers. I first heard of him as a jazz player in the early 90's. I've seen him play jazz and was absolutely blown away. He's such a passionate player – paying tribute to the legacy of music while still having his own voice. That's VERY difficult to do in jazz music because the legacy is so rich.
BUT THEN, I heard him playing with Seal. I didn't know how versatile. Again, blown away.
AND THEN, I heard him on an Emmylou Harris (folk singer) album.
AND THEN, I heard him with Joni Mitchell.
This guy can do anything and still sound like himself. That is incredibly rare and very special when you come across it.
THEN, he decides to make an album as a singer/songwriter. Of course, I immediately bought it and again, I am blown away. Great songs, great guitar playing, great singing (very cool sounding voice) and, of course, great drumming. I think Brian was blessed with severe talent and a wonderful soul. He is also a part of the Black Dub group I've sent previously. Enjoy.
Wow, did that week go fast or what. Hot and fast. The only way to recover from that kind of week: relax with a good book. So, now that you know what I'm doing today, well, for as long as I can anyways 🙂 below I have as many fabulous blogs as I was able to read this week. And Jeff is finally back this week. His music pick this week even has a follow-up pick for next week.
Kara Lennox, a.k.a. Karen Leabo was at Writers In The Storm blog! : Is Your Conflict Strong Enough?
From @smoulderingsea #editortips on 7/3/12 : Using "S/he could tell that…" to interpret another character's actions is a cheap way to avoid breaking POV.
From @smoulderingsea #editortips on 7/2/12: Challenge yourself to write a query pitch/blurb in only 150 words. It'll force you to cut out anything extraneous and focus.
Really great drummers who are also really great singer/songwriter/guitarists.
After having seen them live together, we both know just HOW MUCH they rock.
What I really like about Dave Grohl's approach is that he released the first album under the band name with no attention to himself. He could have easily used his post Nirvana fame to push the project through, so to speak. Instead, he decided to let the music do the talking. I think that's admirable, but I also think it was a smart move. It gave people the chance to judge the music purely on…the music. What a concept! No preconceived notions or other celebrity crap – just music.
Over the years, the band has been extremely successful at taking Dave's songs and making them their own. I think this album is one of the best examples of this. They all play their roles to a perfection and sound like a BAND.
It's a week of transitions for me, but one thing that doesn't change: I'm still learning tons from my blog reads. Good stuff this we folks. Hubs is getting another week off, but I've picked something for you.
Janice Hardy on The Other Side of the Story : The Great Twitter Experiment: What Does "More Tweets" Really Get You?
I found this site from QueryTracker's post Question: is anyone familiar with SmartEdit? It's currently a free product.
The hubs was given another pass this week, another crazy gigging week for him. Don't feel bad for him, he had a ton of fun, we just didn't get to see a lot him, bummer.
Happy Saturday and thanks for stopping by today. I've got some of my favorite links of the week for you, but I've given the hubs the week of from his music picks. He's been working hard all week so I guess that's okay 😉 Instead I've picked an audition from this years So You Think You Can Dance.
Lisa Burstein : PRETTY AMY Original Query Letter AND Query Tips!
Lots of memorable auditions this year. This one stands out because she's a mommy who has not given up on her dream. Listen to her story, watch her beautiful moves, and stay till the end, because her daughter dances too.


text:
\section{Introduction}

Let $\C$ be the complex plane and $\alpha$ be a positive parameter that is fixed
throughout the paper. Let
$$d\lambda_{\alpha}(z)=\frac{\alpha}{\pi}e^{-\alpha|z|^2}\,dA(z)$$
be the Gaussian measure, where $dA$ is the Euclidean area measure. A calculation with
polar coordinates shows that $d\lambda_{\alpha}$ is a probability measure.

The Fock space $F^2_{\alpha}$ consists of all entire functions $f$ in $L^2(\C,d\lambda_{\alpha})$. It is easy to show that $F^2_{\alpha}$ is a closed subspace
of $L^2(\C,d\lambda_{\alpha})$ and so is a Hilbert space with the inherited inner product
$$\langle f,g\rangle=\int_{\C}f(z)\overline{g(z)}d\lambda_{\alpha}(z).$$
In fact, $F^2_\alpha$ is a reproducing kernel Hilbert space whose kernel function is given by $$K_w(z)=K(z,w)=e^{\alpha z\overline{w}}.$$
The norm of functions in $L^2(\C,\dla)$ will simply be denoted by $\|f\|$. The norm of
functions in $f\in L^p(\C,\dla)$ will be denoted by $\|f\|_p$.

We study linear operators (not necessarily bounded) on the Fock space. Throughout the
paper we let $\calD$ denote the set of all finite linear combinations $f$ of kernel functions
in $F^2_\alpha$:
$$f(z)=\sum_{k=1}^Nc_ke^{\alpha z\overline w_k}.$$
It is well known that $\calD$ is a dense linear subspace of $F^2_\alpha$. See \cite{Z3}
for example. We also assume that the domain of every linear operator that appears in the
paper contains $\calD$. Using the relation $\langle SK_z,K_w\rangle=\langle K_z,S^*K_w\rangle$
we see that we can also assume that the domain of $S^*$ contains $\calD$ as well. One additional
standing assumption we make is that the function $z\mapsto SK_z$ is conjugate analytic.

Our main focus here is the boundedness and compactness of operators on $F^2_\alpha$.
To state our main results, we need to introduce a class of unitary operators on $F^2_\alpha$.
More specifically, for any $z\in\C$, let $\varphi_z$ denote the analytic self-map of $\C$
defined by $\varphi_z(w)=z-w$, let $k_z$ denote the normalized reproducing kernel
defined by
$$k_z(w)=K(w,z)/\sqrt{K(z,z)}=e^{-\frac\alpha2|z|^2+\alpha z\overline w},$$
and let $U_z$ denote the operator on $F^2_\alpha$ defined by $U_zf=f\circ\varphi_zk_z$.
Each $k_z$ is a unit vector in $F^2_\alpha$. It follows easily from a change of variables
that each $U_z$ is a self-adjoint unitary operator on $F^2_\alpha$. See \cite{Z3}.

For any $z\in\C$ and any linear operator $S$ on $F^2_\alpha$ let $S_z=U_zSU_z$. It is easy
to check that each $U_z$ maps $\calD$ onto $\calD$ (see Lemma~\ref{lem7}), so the domain
of each $S_z$ contains $\calD$ whenever the domain of $S$ contains $\calD$.

Each operator $S$ on $F^2_\alpha$ also induces a function $\widetilde S$ on $\C$, namely,
$$\widetilde S(z)=\langle Sk_z,k_z\rangle,\qquad z\in\C.$$
We call $\widetilde S$ the Berezin transform of $S$. Since each $k_z$ is a unit vector,
$\widetilde S$ is bounded whenever $S$ is bounded, and $\|\widetilde S\|_\infty\le\|S\|$.
Also, $k_z\to0$ weakly in $F^2_\alpha$ as $z\to\infty$, so $\widetilde S(z)\to0$ as
$z\to\infty$ whenever $S$ is compact on $F^2_\alpha$.

We can now state the main results of the paper.

\begin{tha}
If there exist some $p>2$ and $C>0$ such that $\|S_z1\|_p\le C$ for all $z\in\C$, then
the operator $S$ is bounded on $F^2_\alpha$.
\label{tha}
\end{tha}

\begin{thb}
If there exists some $p>2$ such that $\|S_z1\|_p\to0$ as $z\to\infty$, then $S$ is
compact on $F^2_\alpha$.
\label{thb}
\end{thb}

\begin{thc}
Suppose that there exist some $p>2$ and $C>0$ such that $\|S_z1\|_p\le C$ for all $z\in\C$.
Then $S$ is compact if and only if $\widetilde S(z)\to0$
as $z\to\infty$.
\label{thc}
\end{thc}

As an example, we will apply these results to the study of Toeplitz operators on
$F^2_\alpha$.

The condition $\|S_z1\|_p\le C$ was first introduced in \cite{AZ} and
further studied in \cite{MZ}. An analogue of Theorem C was proved in \cite{MZ}
in the context of Bergman spaces on the unit disk. The papers \cite{CIL,DT,Zor} also
explore the condition $\|S_z1\|_p\le C$.

Our approach here is different from those in the papers mentioned above, although
a key idea from \cite{AZ,MZ} will be used. One of the novelties here is that there is
no need for us to use Schur's test.

A major difference exists between the Bergman space setting and the current one.
More specifically, in the Bergman space setting, there is a certain cut-off requirement,
namely, $p$ cannot be too close to $2$. In fact, it was shown in \cite{MZ} that $p$ must
be greater than $3$ in the case of operators on the Bergman space of the unit disk.
However, the cut-off requirement disappears in the Fock space setting; any $p>2$ will
work. This is not entirely surprising; some similar situations were pointed out and
explained in the book \cite{Z3}.

This work was done while the first named author was visiting the
State University of New York at Albany. He wishes to thank the Department of Mathematics
and Statistics at SUNY-Albnay for hosting his visit. The authors would also like to thank
Josh Isralowitz and Haiying Li for helpful discussions.

\section{A sufficient condition for boundedness}

We prove Theorem A in this section. The following lemma will be used several times
in the paper.

\begin{lem}
For any $p>0$ we have
$$|f(z)|\le\left(\frac\beta\alpha\right)^{\frac1p}\|f\|_pe^{\frac\beta2|z|^2}$$
for all entire functions $f\in L^p(\C,\dla)$ and $z\in\C$, where $\beta=2\alpha/p$.
\label{lem1}
\end{lem}

\begin{proof}
It is clear that
$$\|f\|^p_p=\frac\alpha\pi\inc|f(z)|^pe^{-\alpha|z|^2}\,dA(z)=\frac\alpha\beta\cdot
\frac\beta\pi\inc\left|f(z)e^{-\frac\beta2|z|^2}\right|^p\,dA(z).$$
The desired estimate then follows from Corollary 2.8 in \cite{Z3}.
\end{proof}

We will also need the following estimate several times later on.

\begin{lem}
Suppose $p>2$ and $S$ is a linear operator on $F^2_\alpha$. Then
$$|\langle SK_w,K_z\rangle|\le\|S_w1\|_pe^{\frac\alpha2(|z|^2+|w|^2)-\sigma|z-w|^2}$$
for all $w$ and $z$ in the complex plane, where $\beta=2\alpha/p$ and $\sigma
=(\alpha-\beta)/2$. Consequently, if $\|S_w1\|_p\le C$ for some
constant $C>0$ and all $w\in\C$, then for the same constant $C$ we have
$$|\langle SK_w,K_z\rangle|\le Ce^{\frac\alpha2(|z|^2+|w|^2)-\sigma|z-w|^2}$$
for all $z$ and $w$ in $\C$.
\label{lem2}
\end{lem}

\begin{proof}
Recall that
$$S_w1(z)=(U_wSU_w1)(z)=(U_wSk_w)(z)=k_w(z)(Sk_w)(w-z).$$
By Lemma~\ref{lem1}, we have
$$|k_w(z)(Sk_w)(w-z)|\le\left(\frac\beta\alpha\right)^{\frac1p}\,\|S_w1\|_p\,
e^{\frac\beta2|z|^2}\le\|S_w1\|_p\,e^{\frac\beta2|z|^2}$$
for all $z$ and $w$, where $\beta=2\alpha/p<\alpha$. Replacing $z$ by $w-z$, using
$$Sk_w(z)=e^{-\frac\alpha2|w|^2}SK_w(z)=e^{-\frac\alpha2|w|^2}\langle SK_w,K_z\rangle,$$
and simplifying the result, we obtain
$$|\langle SK_w,K_z\rangle|\le\|S_w1\|_p\,e^{\frac\alpha2|z|^2+\frac\alpha2|w|^2
-\sigma|z-w|^2}$$
for all $z$ and $w$.
\end{proof}

The following lemma shows that every linear operator on $F^2_\alpha$ can be represented
as an integral operator in a canonical way.

\begin{lem}
Let $S$ be a linear operator on $F^2_\alpha$ and let $T$ be the integral operator
defined on $L^2(\C,\dla)$ by
\begin{equation}
Tf(z)=\inc f(w)\langle SK_w,K_z\rangle\,\dla(w).
\label{eq1}
\end{equation}
Then $S$ is bounded on $F^2_\alpha$ if and only if $T$ is bounded on $L^2(\C,\dla)$.
Furthermore, when either of them is bounded, $S$ is equal to the restriction of $T$
to $F^2_\alpha$.
\label{lem3}
\end{lem}

\begin{proof}
For any fixed $z\in\C$, the function
$$w\mapsto\langle K_z,SK_w\rangle=\langle S^*K_z,K_w\rangle=(S^*K_z)(w)$$
is entire and belongs to $F^2_\alpha$ for any fixed $z\in\C$. Therefore, $Tf=0$ for every
$f\in L^2(\C,\dla)\ominus F^2_\alpha$.

If $S$ is bounded on $F^2_\alpha$ and $f=K_a$ is the reproducing kernel at some point
$a\in\C$, then by the reproducing property of $K_a$,
\begin{eqnarray*}
Tf(z)&=&\inc K(w,a)\langle SK_w,K_z\rangle\,\dla(w)\\
&=&\overline{\inc\langle S^*K_z,K_w\rangle K(a,w)\,\dla(w)}\\
&=&\overline{\langle S^*K_z,K_a\rangle}=\langle SK_a,K_z\rangle\\
&=&SK_a(z)=Sf(z).
\end{eqnarray*}
It follows that $Tf=Sf$ on $\calD$ and $\|Tf\|\le\|S\|\|f\|$ for all $f\in\calD$.
Combining this with the conclusion of the previous paragraph, we conclude that $T$ is
bounded on $L^2(\C,\dla)$ and $S$ is equal to the restriction of $T$ to $F^2_\alpha$.

Conversely, if $T$ is bounded on $L^2(\C,\dla)$ and $f\in\calD$, then
$$Tf(z)=\inc f(w)\overline{S^*K_z(w)}\,\dla(w)=\langle f, S^*K_z\rangle=
\langle Sf,K_z\rangle=Sf(z)$$
for all $z\in\C$. This shows that the restriction of $T$ on $\calD$ coincides with action
of $S$ there. Since $\calD$ is dense in $F^2_\alpha$ and $T$ is bounded, we conclude that
$S$ extends to a bounded linear operator on $F^2_\alpha$.
\end{proof}

We can now prove Theorem A which is the main result of this section.

\begin{thm}
Let $S$ be a linear operator on $F^2_\alpha$. If there are constants $p>2$ and $C>0$
such that $\|S_z1\|_p\le C$ for all $z\in\C$, then $S$ is bounded on $F^2_\alpha$ with
$\|S\|\le(2pC)/(p-2)$.
\label{th4}
\end{thm}

\begin{proof}
By Lemma~\ref{lem3}, it suffices for us to show that the integral operator $T$ defined
by (\ref{eq1}) is bounded on $L^2(\C,\dla)$.

By Lemma~\ref{lem2}, for the same constant $C$ and
$$\sigma=\frac{\alpha-\beta}2=\frac{\alpha(p-2)}{2p},$$
we have
$$|Tf(z)|\le C\inc|f(w)|e^{\frac\alpha2(|z|^2+|w|^2)-\sigma|z-w|^2}\,d\lambda_\alpha(w)$$
for all $z\in\C$. Rewrite this as
$$F(z)\le C_1\inc|f(w)|e^{-\frac\alpha2|w|^2}e^{-\sigma|z-w|^2}\,dA(w),$$
where $C_1=C\alpha/\pi$ and
$$F(z)=|Tf(z)|e^{-\frac\alpha2|z|^2}.$$
By H\"older's inequality
\begin{eqnarray*}
F(z)^2&\le&C_1^2\inc\left|f(w)e^{-\frac\alpha2|w|^2}
\right|^2e^{-\sigma|z-w|^2}\,dA(w)\inc e^{-\sigma|z-w|^2}\,dA(w)\\
&=&C_2\inc\left|f(w)e^{-\frac\alpha2|w|^2}\right|^2e^{-\sigma|z-w|^2}\,dA(w),
\end{eqnarray*}
where
$$C_2=C_1^2\inc e^{-\sigma|u|^2}\,dA(u)=\frac{C_1^2\pi}\sigma.$$
It follows from Fubini's theorem and a change of variables that
$$\inc\left|Tf(z)e^{-\frac\alpha2|z|^2}\right|^2\,dA(z)\le C_3\inc
\left|f(w)e^{-\frac\alpha2|w|^2}\right|^2\,dA(w),$$
where
$$C_3=C_2\inc e^{-\sigma|u|^2}\,dA(u)=\frac{C_2\pi}\sigma
=\left(\frac{2pC}{p-2}\right)^2.$$
This shows that the operator $T$ is bounded on $L^2(\C,d\lambda_\alpha)$ and
$$\|T\|\le\frac{2p}{p-2}\,C.$$
Restricting $T$ to the space $F^2_\alpha$ then yields the desired result for $S$.
\end{proof}

Note that the proof above only depends on the pointwise estimate derived
in Lemma~\ref{lem2}, not the full assumption about the norms $\|S_z1\|_p$.

\section{Sufficient conditions for compactness}

In this section we present two sufficient conditions for an operator on $F^2_\alpha$
to be compact. The first condition is the little oh version of the condition in
Theorem A, while the second condition is a natural deviation of the first one.

We begin with Theorem B, the companion result of Theorem A, which
we restate as follows.

\begin{thm}
Let $S$ be a linear operator on $F^2_\alpha$ and $p>2$. If $\|S_z1\|_p\to0$ as
$z\to\infty$, then $S$ is compact on $F^2_\alpha$.
\label{th5}
\end{thm}

\begin{proof}
It follows from our standing assumptions on $S$ that the condition $\|S_z1\|_p\to0$
as $z\to\infty$ implies that $\|S_z1\|_p$ is bounded in $z$. Therefore, by Theorem~\ref{th4},
$S$ is already bounded on $F^2_\alpha$. By Lemma~\ref{lem3}, it suffices for us to show
that the integral operator $T$ defined by (\ref{eq1}) is compact on $L^2(\C,\dla)$.
We do this using an approximation argument.

For any $r>0$ let us consider the integral operator $T_r$ defined on $L^2(\C,\dla)$ by
\begin{eqnarray*}
T_rf(z)&=&\int_{|w|<r}f(w)\langle SK_w,K_z\rangle\,\dla(w)\\
&=&\inc f(w)\chi_r(w)\langle SK_w,K_z\rangle\,\dla(w),
\end{eqnarray*}
where $\chi_r$ is the characteristic function of the disk $\{z\in\C:|z|<r\}$.
It follows easily from Lemma~\ref{lem2} that
$$\inc\inc|\chi_r(w)\langle SK_w,K_z\rangle|^2\,\dla(z)\,\dla(w)<\infty.$$
Thus each $T_r$ is Hilbert-Schmidt. In particular, each $T_r$ is compact on
$L^2(\C,\dla)$.

Let $D_r=T-T_r$. Then
\begin{eqnarray*}
D_rf(z)&=&\inc f(w)(1-\chi_r(w))\langle SK_w,K_z\rangle\,\dla(w)\\
&=&\int_{|w|>r}f(w)\langle SK_w,K_z\rangle\,\dla(w).
\end{eqnarray*}
We are going to show that $\|D_r\|\to0$ as $r\to\infty$, which would imply that $T$ is
compact.

Given any $\varepsilon>0$, choose a positive number $R$ such that $\|S_w1\|_p<
\varepsilon$ for all $|w|>R$. By Lemma~\ref{lem2}, for any $r>R$ we have
$$|1-\chi_r(w)||\langle SK_w,K_z\rangle|\le\varepsilon e^{\frac\alpha2(|z|^2+|w|^2)
-\sigma|z-w|^2}$$
for all $z$ and $w$ in $\C$ (just consider the cases $|w|\le r$ and $|w|>r$ separately).
It follows from the proof of Theorem~\ref{th4} that there is
a positive constant $C$, independent of $\varepsilon$ and $r$, such that
$\|D_r\|\le C\varepsilon$ for all $r>R$. This shows that $\|D_r\|\to0$ as $r\to\infty$
and completes the proof of the theorem.
\end{proof}

Recall from the definition of $S_z$ and $U_z$ that
$$S_z1=U_zSU_z1=U_zSk_z,\qquad z\in\C.$$
Since each $U_z$ is a unitary operator on $F^2_\alpha$, the condition $\|S_z1\|\le C$
is the same as $\|Sk_z\|\le C$. However, $U_z$ is not isometric on $L^p(\C,\dla)$ when
$p\not=2$, so it is natural for us to consider the condition $\|Sk_z\|_p\le C$.

\begin{pro}
Let $S$ be a linear operator on $F^2_\alpha$ and $p>2$. If there is a constant $C>0$
such that $\|Sk_z\|_p\le C$ and $\|S^*k_z\|_p\le C$ for all $z\in\C$, then $S$ is
Hilbert-Schmidt on $F^2_\alpha$. In particular, $S$ is compact.
\label{pro6}
\end{pro}

\begin{proof}
By Lemma~\ref{lem1}, the assumption on $\|Sk_w\|_p$ implies that there exists another
positive constant $C$ such that
$$|(Sk_w)(z)|\le Ce^{\frac\beta2|z|^2},\qquad z,w\in\C,$$
where $\beta=2\alpha/p<\alpha$. This can be rewritten as
\begin{equation}
|\langle SK_w,K_z\rangle|\le Ce^{\frac\alpha2|w|^2+\frac\beta2|z|^2}
\label{eq2}
\end{equation}
for all $z$ and $w$. Similarly, the assumption on $\|S^*k_w\|_p$ implies that
\begin{equation}
|\langle SK_w,K_z\rangle|\le Ce^{\frac\alpha2|z|^2+\frac\beta2|w|^2}
\label{eq3}
\end{equation}
for all $z$ and $w$.

Multiply the inequalities in (\ref{eq2}) and (\ref{eq3}) and then take the square
root on both sides. The result is
$$|\langle SK_w,K_z\rangle|\le Ce^{\frac\delta2(|z|^2+|w|^2)}$$
for all $z$ and $w$, where $\delta=(\alpha+\beta)/2<\alpha/2$. It follows from this that
$$\inc\inc\left|\langle SK_w,K_z\rangle\right|^2\,\dla(w)\,\dla(z)<\infty,$$
so that the integral operator $T$ defined by
$$Tf(z)=\inc f(w)\langle SK_w,K_z\rangle\,d\lambda_\alpha(w)$$
is Hilbert-Schmidt on $L^2(\C,d\lambda_\alpha)$. Since $S$ is the restriction of $T$ on
$F^2_\alpha$, we conclude that $S$ is Hilbert-Schmidt on $F^2_\alpha$.
\end{proof}

Once again, we only used the pointwise estimates deduced from the assumptions on
$\|Sk_z\|_p$ and $\|S^*k_z\|_p$.

\section{Compactness via the Berezin transform}

In this section we show that, under the assumption of Theorem A, the
compactness of a linear operator on $F^2_\alpha$ can be characterized in terms of
its Berezin transform.

\begin{lem}
For any $a$ and $w$ in the complex plane we have
$$U_aK_w=\overline{k_a(w)}K_{\varphi_a(w)},\quad U_ak_w=\beta k_{\varphi_a(w)},
\quad \widetilde S\circ\varphi_a=\widetilde{S_a},$$
where $\beta$ is a unimodular constant depending on $a$ and $w$.
\label{lem7}
\end{lem}

\begin{proof}
The first identity follows from the definition of $U_a$ and the explicit form of the
kernel function. The second identity follows from the first one with
$$\beta=e^{\frac\alpha2(a\overline w-\overline aw)}.$$
By the definition of the Berezin transform, the definition of $S_a$, and the second
identity that we have already proved, we have
\begin{eqnarray*}
\widetilde{S_a}(w)&=&\langle S_ak_w,k_w\rangle=\langle U_aSU_ak_w,k_w\rangle\\
&=&\langle SU_ak_w,U_ak_w\rangle=|\beta|^2\langle Sk_{\varphi_a(w)},k_{\varphi_a(w)}\rangle\\
&=&\widetilde S(\varphi_a(w)).
\end{eqnarray*}
This proves the third identity.
\end{proof}

\begin{lem}
Let $S$ be a linear operator on $F^2_{\alpha}$. Suppose that there are constants $p>2$
and $C>0$ such that $\|S_z1\|_p\le C$ for all $z\in\C$. Then $\widetilde{S}(w)\to0$
as $w\to\infty$ if and only if for every (or some) $2<p'<p$ we have $\|S_w 1\|_{p'}\to0$
as $w\to\infty$.
\label{lem8}
\end{lem}

\begin{proof}
If for some $p'\in (2,p)$ we have $\|S_w 1\|_{p'}\rightarrow 0$ as $w\rightarrow \infty$,
then by H\"older's inequality,
$$|\widetilde{S}(w)|=|\langle S_w 1, 1\rangle| \leq \|S_w 1\|_{p'}\rightarrow 0$$
as $w\rightarrow \infty$.

Next, suppose $\widetilde{S}(w)\rightarrow 0$ as $w\rightarrow \infty$ and fix any
$p'\in (2,p)$. We proceed to show that $\|S_w 1\|_{p'}\rightarrow 0$ as $w\rightarrow\infty$.

For any $a$ and $z$ we have
$$\widetilde{S}(\varphi_z(a))=\widetilde{S_z}(a)=e^{-\alpha|a|^2}\langle S_z K_a,K_a \rangle,$$
where
$$K_a(u)=e^{\alpha u\overline{a}}=\sum_{k=0}^{\infty}\frac{\alpha^k}{k!}u^k \overline{a}^k.$$
By the proof of Lemma 6.26 in \cite{Z3}, starting at line 4 from the bottom of page 240 and
finishing at line 3 from the top of page 242, with $\widetilde f$ replaced by $\widetilde S$ and
$T_{f\circ\varphi_z}$ replaced by $S_z$, we will have
$$\lim_{z\to\infty}\langle S_z1, z^n\rangle=0$$
for every $n\ge0$. Since the polynomials are dense in $F^2_\alpha$, we conclude that
$S_z1\to 0$ weakly in $F^2_\alpha$ as $z\to\infty$. In particular, for every $w\in\C$,
$S_z1(w)\to 0$ as $z\to\infty$.

Let $s=p/p'>1$ and choose $t>1$ such that $1/s+1/t=1$. For any measurable set $E$ we have
\begin{eqnarray*}
\int_E|S_z1(w)|^{p'}\,d\lambda_\alpha(w)&\le&\left[\int_E|S_z1(w)|^p\,d\lambda_\alpha(w)
\right]^{\frac1s}\left[\int_E d\lambda_\alpha(w)\right]^{\frac1t}\\
&\le&\|S_z1\|_p^{p'}\left[\lambda_\alpha(E)\right]^{\frac1t}.
\end{eqnarray*}
Since $\|S_z1\|_p\le C$ for all $z\in\C$, this shows that the family $\{|S_z1|^{p'}:z\in\C\}$
is uniformly integrable. By Vitali's Theorem,
$$\lim_{z\to\infty}\inc|S_z1(w)|^{p'}\,d\lambda_\alpha(w)=0.$$
This completes the proof of the lemma.
\end{proof}

We can now prove Theorem C, the main result of this section, which we restate as follows.

\begin{thm}
Suppose $S$ is a linear operator on $F^2_\alpha$, $p>2$, $C>0$, and $\|S_z1\|_p\le C$
for all $z\in\C$. Then $S$ is compact on $F^2_\alpha$ if and only if $\widetilde S(z)
\to0$ as $z\to\infty$.
\label{th9}
\end{thm}

\begin{proof}
By Theorem~\ref{th4}, $S$ is bounded on $F^2_\alpha$. If $S$ is further compact, then
$\widetilde S(z)=\langle Sk_z,k_z\rangle\to0$ as $z\to\infty$, because $k_z\to0$ weakly
in $F^2_\alpha$ as $z\to\infty$.

Conversely, if $\widetilde S(z)\to0$ as $z\to\infty$, it follows from Lemma~\ref{lem8}
that $\|S_z1\|_{p'}\to0$ as $z\to\infty$, where $p'$ is any fixed number strictly between
$2$ and $p$. This together with Theorem~\ref{th5} then implies that $S$ is compact.
\end{proof}

\section{An application to Toeplitz operators}

Let $P:L^2(\C,\dla)\to F^2_\alpha$ denote the orthogonal projection. If
$\psi\in L^\infty(\C)$, we can define a linear operator $T_\psi$ on $F^2_\alpha$ by
$T_\psi f=P(\psi f)$. It is clear that $T_\psi$ is bounded and $\|T_\psi\|\le\|\psi\|_\infty$.
It is also easy to verifty that
$$(T_\psi)_z=U_zT_\psi U_z=T_{\psi\circ\varphi_z}$$
for all $z\in\C$. In particular, $(T_\psi)_z1=P(\psi\circ\varphi_z)$, or
$$(T_\psi)_z1(w)=\inc K(w,u)\psi(z-u)\,\dla(u),\qquad w\in\C.$$
It follows that
\begin{eqnarray*}
|(T_\psi)_z1(w)|&\le&\|\psi\|_\infty\inc|e^{\alpha w\overline u}|\,\dla(u)\\
&=&\|\psi\|_\infty\inc\left|e^{\alpha(w/2)\overline u}\right|^2\,\dla(u)\\
&=&\|\psi\|_\infty e^{\alpha|w/2|^2}=\|\psi\|_\infty e^{\frac\alpha4|w|^2}
\end{eqnarray*}
for all $w\in\C$. This shows that
$$\sup_{z\in\C}\inc\left|(T_\psi)_z1\right|^p\,\dla<\infty$$
whenever $0<p<4$. Therefore, the assumption in Theorem~\ref{th9} is satisfied for each
$p\in(2,4)$. Consequently, we arrive at the well-known result that such a Toeplitz operator
is compact if and only if its Berezin transform vanishes at $\infty$. See \cite{CIL,Z3}.

Using the integral representation for the orthogonal projection, it is possible to
define Toeplitz operators $T_\psi$ for functions $\psi$ that are not necessarily
bounded. In particular, $T_\psi$ is well defined on $\calD$ whenever $\psi$ belongs
to the space BMO used in Section 6.4 of \cite{Z3}. For such a symbol function $\psi$,
Lemma 6.25 of \cite{Z3} states that
$$|(T_\psi)_z1(w)|\le Ce^{\frac\alpha4|w|^2},\qquad w\in\C,$$
whenever $\widetilde\psi$ is bounded, which implies that $\|(T_\psi)_z1\|_p\le C$ for
$2<p<4$. This together with the arguments in the previous
paragraph shows that, for such $\psi$, the operator $T_\psi$ is bounded if and only
if its Berezin transform is bounded; and $T_\psi$ is compact if and only if its
Berezin transform vanishes at $\infty$. See \cite{CIL,Z3} again.

The Berezin transform of $T_\psi$ is usually written as
$\widetilde\psi$ or $B_\alpha\psi$. It is easy to see that
$$B_\alpha\psi(z)=\inc\psi(z-w)\,\dla(w)=\frac\alpha\pi\inc\psi(w)e^{-\alpha|z-w|^2}
\,\dla(w)$$
for $z\in\C$. See \cite{Z3} for more information about the Berezin transform which is
also called the heat transform in many articles.

The arguments above can also be extended to operators of the form
$T=T_{\psi_1}\cdots T_{\psi_n}$, where each $\psi_k$ belongs to $L^\infty(\C)$.
In fact, in the case $S=T_{\psi_1}T_{\psi_2}$, we have
$$S_z1=P\left[\psi_1\circ\varphi_z(T_{\psi_2})_z1\right].$$
Using the integral representation for the outside $P$ and the pointwise estimate we
already obtained for $(T_{\psi_2})_z1$, we arrive at
$$|S_z1(w)|\le C\inc e^{\frac\alpha4|u|^2}|K(w,u)|\,\dla(u)\le C_1e^{\frac\alpha3|w|^2}.$$
This implies that
$$\sup_z\|S_z1\|_p<\infty,\qquad 2<p<3.$$
More generally, if $\sigma>2$, then
$$\inc e^{\frac\alpha\sigma|u|^2}|K(w,u)|\,\dla(u)\le Ce^{\frac\alpha{\sigma'}|w|^2},$$
with
$$\sigma'=4\left(1-\frac1\sigma\right)>2.$$
So by mathematical induction, each operator $S=T_{\psi_1}\cdots T_{\psi_n}$ satisfies
the pointwise estimate
$$|S_z1(w)|\le Ce^{\frac\alpha\sigma|w|^2},\qquad w\in\C,$$
for some $\sigma>2$. It follows that
$$\sup_z\|S_z1\|_p<\infty,\qquad p\in(2,\sigma).$$

Going one step further, we can also extend the arguments above to operators on
$F^2_\alpha$ that are finite sums of finite products of Toeplitz operators.

\section{Further results and remarks}

For any $p>0$ the Fock space $F^p_\alpha$ is defined to be the set of all entire
functions $f$ such that $f(z)e^{-\frac\alpha2|z|^2}$ belongs to $L^p(\C,dA)$. The
norm in $F^p_\alpha$ is defined by
$$\|f\|^p_{p,\alpha}=\frac{p\alpha}{2\pi}\inc\left|f(z)e^{-\frac\alpha2|z|^2}
\right|^p\,dA(z).$$
It is clear that when $p=2$, the definition here is consistent with the definition
of $F^2_\alpha$ in the Introduction. More generally, we have
$$F^p_\alpha=H(\C)\cap L^p(\C,d\lambda_\beta),\qquad \beta=\frac{p\alpha}2,$$
where $H(\C)$ is the space of all entire functions. Equivalently,
$$H(\C)\cap L^p(\C,\dla)=F^p_\beta,\qquad \beta=\frac{2\alpha}p.$$

Although both $F^p_\alpha$ and $H(\C)\cap L^p(\C,\dla)$ are natural extentions of
the Fock space $F^2_\alpha$, in most cases it is much more beneficial, more
convenient, and more natural to use $F^p_\alpha$ instead of the other one. Of course
there are exceptions, the results of this paper being one of them. Nevertheless,
the following question still seems natural: What happens if we replaced the
condition $\|S_z1\|_p\le C$ by the condition $\|S_z1\|_{p,\alpha}\le C$? We do not
know the answer. But the techniques used in the paper would certainly not work,
because the optimal pointwise estimate for functions in $F^p_\alpha$ is given by
$$|f(z)|\le\|f\|_{p,\alpha}e^{\frac\alpha2|z|^2},\qquad z\in\C.$$
See Corollary 2.8 in \cite{Z3}. We needed a certain decrease in the exponent in
order to perform the analysis in Sections 2--4.

In the case of $S=T_\psi$, where $\psi\in L^\infty(\C)$, we already showed that
$$\sup_{z\in\C}\|(T_\psi)_z1\|_p<\infty,\qquad \sup_{z\in\C}\|(T_\psi^*)_z1\|_p<\infty,$$
for $0<p<4$. On the other hand, for every $p\in[1,\infty)$, the projection $P$ is
bounded from the space
$$L^p_\alpha(\C)=\left\{f:f(z)e^{-\frac\alpha2|z|^2}\in L^p(\C,dA)\right\}$$
onto the space $F^p_\alpha$; see \cite{Z3} for example. It follows from this and the
identity $(T_\psi)_z1=P(\psi\circ\varphi_z)$ that
$$\sup_{z\in\C}\|(T_\psi)_z1\|_{p,\alpha}<\infty,\qquad
\sup_{z\in\C}\|(T_\psi^*)_z1\|_{p,\alpha}<\infty,$$
for all $1\le p<\infty$. Thus the condition $\|S_z1\|_p\le C$ appears stronger (or
more difficult to satisfy) than the condition $\|S_z1\|_{p,\alpha}\le C$. This is
easily confirmed by the elementary continuous embedding
$$H(\C)\cap L^p(\C,\dla)=F^p_\beta\subset F^p_\alpha,$$
where $\beta=(2\alpha)/p<\alpha$ for $p>2$.

The example in the previous section of Toeplitz operators on $F^2_\alpha$ induced by
bounded symbols shows that the condition $\|S_z1\|_p\le C$ is a meaningful one. We just
do not know what the weaker condition $\|S_z1\|_{p,\alpha}\le C$ would imply. But there
is more we can say.

For each $z\in\C$ the operator $U_z$ is actually a surjective isometry on each
$F^p_\alpha$, and $k_z$ is actually a unit vector in $F^p_\alpha$. Therefore, the
condition $\|S_z1\|_{p,\alpha}\le C$ is the same as $\|Sk_z\|_{p,\alpha}\le C$.
If there exists a bounded linear operator $S$ on $F^p_\alpha$, $2<p<\infty$, such
that $S$ is not bounded on $F^2_\alpha$, then the condition $\|S_z1\|_{p,\alpha}\le C$
would not imply the boundedness of $S$ on $F^2_\alpha$. Although we do not have an
example at hand, this seems very plausible to us.

Note that the proof of Theorem~\ref{th4} amounts to showing that the integral
operator $T$ defined by
$$Tf(z)=\inc f(w)H(z,w)\,d\lambda_\alpha(w)$$
is bounded on $L^2(\C,d\lambda_\alpha)$, where
$$H(z,w)=e^{\frac\alpha2(|z|^2+|w|^2)-\sigma|z-w|^2}.$$
Since $f\in L^2(\C,d\lambda_\alpha)$ if and only if the function
$f(w)e^{-\frac\alpha2|w|^2}$ is in $L^2(\C,dA)$, and since
$$e^{-\frac\alpha2|z|^2}Tf(z)=\frac\alpha\pi\inc\left[f(w)e^{-\frac\alpha2|w|^2}\right]
e^{-\sigma|z-w|^2}\,dA(w),$$
we see that the operator $T$ on $L^2(\C,d\lambda_\alpha)$ is unitarily equivalent to
the Berezin transform $B_\sigma$ as an operator on $L^2(\C,dA)$. Recall that
$$B_\sigma f(z)=\frac\sigma\pi\inc f(w)e^{-\sigma|z-w|^2}\,dA(w).$$
The boundedness of $B_\sigma$ on $L^2(\C,dA)$ is actually a known result.
See \cite{Z3} for example.

A natural question here is the following: is the Berezin transform $B_\sigma$
compact on $L^2(\C,dA)$? Since the proof of Theorem~\ref{th4} along with the fact that
$\|(T_\psi)_z1\|_p\le C$ for $2<p<4$ shows that every
Toeplitz operator $T_\psi$ on $F^2_\alpha$, $\psi\in L^\infty(\C)$, is dominated by
$B_\sigma$ as an operator on $L^2(\C,dA)$, and it is very easy to see that there are
such Toeplitz operators that are not compact, we see that $B_\sigma$ cannot possibly
be compact on $L^2(\C,dA)$. To see this more directly, we consider the sequence
$\{\chi_n\}$ of characteristic functions of the disks $B(n,1)$. It is easy to see
that $\{\chi_n\}$ converges to $0$ weakly in $L^2(\C,dA)$. But
$$B_\sigma\chi_n(z)=\frac\sigma\pi\int_{B(0,1)}e^{-\sigma|z-n-w|^2}\,dA(w)=g(z-n),$$
where
$$g(z)=\frac\sigma\pi\int_{B(0,1)}e^{-\sigma|z-w|^2}\,dA(w).$$
By translation invariance, the norm of each $B_\sigma\chi_n$ in $L^2(\C,dA)$ is equal
to that of $g$. Thus $\|B_\sigma\chi_n\|_{L^2(\C,dA)}\not\to0$ as $n\to\infty$, so
$B_\sigma$ is not compact on $L^2(\C,dA)$.

Our arguments can also be adapted to work for Bergman spaces on the unit ball $\bn$ in
$\cn$. More specifically, for any $\alpha>-1$ we consider the weighted volume measure
$$dv_\alpha(z)=c_\alpha(1-|z|^2)^\alpha\,dv(z),$$
where $dv$ is ordinary volume measure on $\bn$ and $c_\alpha$ is a normalizing constant
chosen so that $v_\alpha(\bn)=1$. For any $p>0$ the spaces
$$A^p_\alpha=H(\bn)\cap L^p(\bn,dv_\alpha)$$
are called (weighted) Bergman spaces, where $H(\bn)$ is the space of all holomorphic
functions on $\bn$.

The space $A^2_\alpha$ is a reproducing kernel Hilbert space whose reproducing kernel
is given by
$$K(z,w)=\frac1{(1-\langle z,w\rangle)^{n+1+\alpha}}.$$
The normalized reproducing kernels are still defined by
$$k_z(w)=\frac{K(w,z)}{\sqrt{K(z,z)}}=\frac{(1-|z|^2)^{\frac{n+1+\alpha}2}}{(1-
\langle z,w\rangle)^{n+1+\alpha}}.$$

For every $z\in\bn$ there is also a canonical involutive automorphism $\varphi_z$ of
the unit ball $\bn$, and an associated self-adjoint unitary operator $U_z$ can be defined
on $A^2_\alpha$ by $U_zf=f\circ\varphi_zk_z$. If $S$ is a linear operator on $A^2_\alpha$,
not necessirly bounded, whose domain contains all finite linear combinations of kernel
functions, then we can still consider $S_z=U_zSU_z$.

The optimal pointwise estimate for functions in Bergman spaces is given by
$$|f(z)|\le\frac{\|f\|_{A^p_\alpha}}{(1-|z|^2)^{\frac{n+1+\alpha}p}}.$$
See \cite{Z2} for this and the results quoted in the previous two paragraphs. It
follows from the proof of Lemma~\ref{lem2} that the condition
$$\sup_{z\in\bn}\|S_z1\|_{A^p_\alpha}<\infty,$$
where $p>2$, implies the inequality
$$|\langle SK_w,K_z\rangle|\le\frac{C|1-\langle z,w\rangle|^{\left(\frac2p
-1\right)(n+1+\alpha)}}{(1-|z|^2)^{\frac{n+1+\alpha}p}(1-|w|^2)^{\frac{n+1+\alpha}p}}.$$
Our techniques here can be adapted to show that for
\begin{equation}
p>2+\frac{2n}{\alpha+1},
\label{eq4}
\end{equation}
the condition $\|S_z1\|_{A^p_\alpha}\le C$ implies that the operator $S$ is bounded
on $A^2_\alpha$. Similarly, the condition
$$\lim_{|z|\to1^-}\|S_z1\|_{A^p_\alpha}=0$$
implies that the operator $S$ is not only bounded but also compact on $A^2_\alpha$.
Furthermore, under the assumption $\|S_z1\|_{A^p_\alpha}\le C$, the compactness of
$S$ on $A^2_\alpha$ is equivalent to the vanishing of the Berezin transform of $S$
on the unit sphere $|z|=1$. We leave the details to the interested reader.

We point out that in the case when $n=1$ and $\alpha=0$,
the restriction $p>4$ in (\ref{eq4}) is not as good as the optimal restriction $p>3$
obtained in \cite{MZ}. The discrepancy stems from the fact that our approach here only
uses pointwise estimates derived from the assumption about norms, while the approach in
\cite{MZ} made full use of the assumption about norms.

We also mention that the conditions
\begin{equation}
\sup_{z\in\bn}\|Sk_z\|_{A^p_\alpha}<\infty,\quad
\sup_{z\in\bn}\|S^*k_z\|_{A^p_\alpha}<\infty,
\label{eq5}
\end{equation}
where $p>2$, imply the inequality
$$|\langle SK_w,K_z\rangle|\le\frac C{(1-|z|^2)^{\frac{n+1+\alpha}{q}}
(1-|w|^2)^{\frac{n+1+\alpha}{q}}},$$
where $q\in(2,p)$ is the exponent given by
$$\frac1{q}=\frac12\left(\frac12+\frac1p\right).$$
If $p$ and $\alpha$ satisfy
$$\alpha+1>\left(\frac12+\frac1p\right)(n+1+\alpha),$$
then the conditions in (\ref{eq5}) imply that $S$ is Hilbert-Schmidt on
$A^2_\alpha$. Obviously, the dependence on $p$ and $\alpha$ in the Bergman space
theory is much more delicate. Again, the interested reader can easily work out the
details by following arguments in previous sections of this paper.

redpajama_set_name: RedPajamaArXiv


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text:
Courses / Undergraduate / English and Spanish (BA)
Typical Offer
AAB AAB (View full entry requirements)
UCAS Course code
Open days and visits Order a prospectus Student life
English and Spanish (BA) starting September 2022 for 4 years
About this course Entry requirements Course structure Modules Learning and assessment Careers Fees, costs and funding How to apply Related courses
Develop your passion for reading and your talent for languages with this English and Spanish degree. Examine writers from around the world in the context of politics, culture, identity and society. At Southampton, you'll study the Spanish language, linguistics and culture, and English together, to improve the way you learn. Your year abroad will give you new perspectives on language, story and identity.
This dynamic course shows you the connections between literature, language and culture. Our English modules cover writing from around the world and the links to politics, the arts, identity and more. You'll study novels, poetry, drama and non-fiction from their early origins to the present day.
In your Spanish studies, you can take modules that feed your love of history and culture, or you may choose to focus on linguistics. You can shape your degree to suit your interests or career aspirations.
You'll spend your third year abroad at one of our partner universities or take a work placement.
As part of this course you can:
use our Centre for Language Study, including a Spanish resources room
join one of 40 student-led performing arts groups
take part in writing workshops at Nuffield Southampton Theatres
use a unique collection of rare books at the Chawton House Library
explore experimental writing with our Entropics events
get one-to-one tutorials on writing from our Royal Literary Fund Fellows
Course location
This course is based at Avenue.
This qualification is awarded by the University of Southampton.
Download the Course Description Document
The Course Description Document details your course overview, your course structure and how your course is taught and assessed.
Changes due to COVID-19
Although the COVID-19 situation is improving, any future restrictions could mean we might have to change the way parts of our teaching and learning take place in 2021 to 2022. We're working hard to plan for a number of possible scenarios. This means that some of the information on this course page may be subject to change.
Find out more on our COVID advice page.
Download 2021-22 Course Description Document
For Academic year 202223
AAB including Grades AB in English Literature (or a related subject*) and Spanish
A-levels additional information
Offers typically exclude General Studies and Critical Thinking. *Related subject includes History, English Language and Literature, English Language or Drama and Theatre Studies.
More information about A-levels
A-levels with Extended Project Qualification
If you are taking an EPQ in addition to 3 A levels, you will receive the following offer in addition to the standard A level offer:
ABB including Grades AB in English Literature (or a related subject*) and Spanish, and grade A in the EPQ
A-levels contextual offer
We are committed to ensuring that all applicants with the potential to succeed, regardless of their background, are encouraged to apply to study with us. The additional information gained through contextual data allows us to recognise an applicant's potential to succeed in the context of their background and experience. Applicants who are highlighted in this way will be made an offer which is lower than the typical offer for that programme, as follows: ABB including English Literature or a related subject* and Spanish
International Baccalaureate Diploma
Pass, with 34 points overall with 17 points at Higher Level, including 6 and 5 at Higher Level in English Literature (or a related subject*) and Spanish
International Baccalaureate Diploma additional information
*Related subject includes History, English Language and Literature, English Language or Drama and Theatre Studies.
More information about International Baccalaureate Diploma
International Baccalaureate contextual offer
We are committed to ensuring that all learners with the potential to succeed, regardless of their background, are encouraged to apply to study with us. The additional information gained through contextual data allows us to recognise a learner's potential to succeed in the context of their background and experience. Applicants who are highlighted in this way will be made an offer which is lower than the typical offer for that programme.
International Baccalaureate Career Programme (IBCP) statement
Offers will be made on the individual Diploma Course subject(s) and the career-related study qualification. The CP core will not form part of the offer. Where there is a subject pre-requisite(s), applicants will be required to study the subject(s) at Higher Level in the Diploma course subject and/or take a specified unit in the career-related study qualification. Applicants may also be asked to achieve a specific grade in those elements. Please see the University of Southampton International Baccalaureate Career-Related Programme (IBCP) Statement for further information. Applicants are advised to contact their Faculty Admissions Office for more information.
More information about BTEC
Select additional entry requirements to display
Show more entry requirements Access to HE Diploma Irish Leaving Certificate Scottish Qualification offers Cambridge Pre-U Welsh Baccalaureate European Baccalaureate
Show more entry requirements
Access to HE Diploma
Irish Leaving Certificate
Scottish Qualification offers
Welsh Baccalaureate
European Baccalaureate
60 credits with a minimum of 45 credits at Level 3, of which 39 must be at Distinction and 6 credits at Merit, to include 6 Distinctions in English Literature (or a related subject*), plus A in A level Spanish
Access to HE additional information
Irish Leaving Certificate (first awarded 2017)
A2 A2 A2 B1 B1 B1 including English Literature (or a related subject*) and Spanish at A2 and B1
H1 H2 H2 H2 H2 H2 including English Literature (or a related subject*) and Spanish
Irish certificate additional information
Scottish Qualification
Offers will be based on exams being taken at the end of S6. Subjects taken and qualifications achieved in S5 will be reviewed. Careful consideration will be given to an individual's academic achievement, taking in to account the context and circumstances of their pre-university education.
Please see the University of Southampton's Curriculum for Excellence Scotland Statement (PDF) for further information. Applicants are advised to contact their Faculty Admissions Office for more information.
D3 D3 M2 in three principal subjects including English Literature (or a related subject*) and Spanish
Cambridge Pre-U additional information
AAB from 3 A levels including Grades AB in English Literature (or a related subject*) and Spanish or AA from two A levels including English Literature (or a related subject*) and Spanish and B from the Advanced Welsh Baccalaureate Skills Challenge Certificate
Welsh Baccalaureate additional information
Welsh Baccalaureate contextual offer
80% overall including grade 8.5 and 8 in English Literature (or a related subject*) and Spanish
Other ways to qualify
GCSE requirements
Applicants must hold GCSE English language (or GCSE English) (minimum grade 4/C) and mathematics (minimum grade 4/C)
Find the equivalent international qualifications for our entry requirements.
If English isn't your first language, you'll need to complete an International English Language Testing System (IELTS) to demonstrate your competence in English. You'll need all of the following scores as a minimum:
IELTS score requirements
We accept other English language tests. Find out which English language tests we accept.
You might meet our criteria in other ways if you do not have the qualifications we need. Find out more about:
our Access to Southampton scheme for students living permanently in the UK (including residential summer school, application support and scholarship)
skills you might have gained through work or other life experiences (otherwise known as recognition of prior learning)
Find out more about our Admissions Policy.
Please contact our enquiries team if you're not sure that you have the right experience or qualifications to get onto this course.
Email: enquiries@southampton.ac.uk
About this course Course structure
Your English modules cover writing from around the world and its connection to politics, the arts, identity and more. You can also study creative writing. Your Spanish studies will include compulsory language modules, linguistics and many options in politics and culture.
The Spanish language modules depend on your ability level. We will put you in the most appropriate stage to develop your spoken and written skills.
Each year you can take modules from subject areas outside English and Spanish. Your personal academic tutor can advise you on module options.
Typically, you'll take an equal number of modules from English and Spanish. You'll choose from modules in linguistics and in the culture and history of Spanish-speaking countries.
You'll gain a foundation in critical thinking, essay writing and joint research. This will help you develop your own views and approaches in the study of literature.
You'll also take a compulsory module for modern language students. It outlines the academic conventions you'll need and offers guidance on study skills.
You'll take a mix of core and optional English modules, including:
Poetic Language
a group research project, including options such as City Writing in the Nineteenth Century, Literature to Save the Planet, or Decadence and Decay at the Fin de Siècle
The Act of the Essay
You can choose modules from across English and Spanish based on your interests and the skills you want to develop. You'll also take a compulsory Spanish language module.
Modules include:
Gender, Race and Nation in Modern Latin America
Myths and Realities of Contemporary Spain
African Worlds
Sweatshops, Sex Workers and Asylum Seekers: World Literature and Visual Culture After Globalisation
Images of Women
A special module will help you plan your year abroad.
You'll spend your third year in a Spanish-speaking country and improve your language and cultural skills.
We'll help you choose a placement abroad that interests you. You can:
study at one of our partner universities
work as an English language assistant in a school
find an approved work placement
During your time away, you'll keep a blog and produce an independent research project in Spanish. It will show original thought and help improve your language.
You'll take a module examining your experiences abroad. This will help you produce an enhanced CV.
You'll write a dissertation on a topic of your choice, from either subject area, to develop your independent research skills. A supervisor with research expertise on your topic will support you.
You'll continue with Spanish language modules and take optional modules from across English, Spanish and other subject areas.
Module options include:
Translation: Theory and Practice
Narrative Non-Fiction: The Interdisciplinary Art
Literatures of Islands and Oceans
Radical England: from Shakespeare to Milton
The EU and European Identity
Want more detail? See all the modules in the course.
Entry requirements Modules
For entry in Academic Year 2022-23
Year 1 modules
You must study the following modules in year 1:
Academic Skills for ML students
This module is designed to ease the transition from A-level to the first year of a single or combined honours degree programme by setting out clearly what we expect of you at undergraduate level and equipping you with the resources to be able to operate a...
English on the Move
English has always been on the move. As a literary language, it has not only travelled from and back to England; lines of influence between texts, authors, publishers, editors, book technologies, and readers traverse the globe in multiple directions, bet...
How do we read poems, and what language can we use to describe our readings? This module will provide a detailed introduction to the particular qualities your ear, eye and brain will need to read poetry more effectively. You will study key features of poe...
Spanish Language Stage 4
The aim of every language course at the University is to enable you to communicate in your target language (TL) at that particular level and in your particular area of interest. We use the word 'communicate' in its widest sense, meaning that you will not ...
The History and Politics of the Hispanic World
This course will introduce students to the major themes in Spanish and Spanish American history and politics over the past five hundred years.
You must also choose from the following modules in year 1:
Applications of Linguistics
This unit will introduce you to the main areas relevant to applied language studies.
Elements of Linguistics - Sound, Structure and Meaning
This module is intended to provide an outline for some of the main aspects of Linguistics.
Humanities, the Human and the Non-Human
This module both challenges and enriches the idea of 'the human' as an idea for 'the humanities'. You will reflect upon 'the human' as a concept that exceeds the individual person in literary, artistic, historical and political texts. Taking this challe...
Literary Transformations
Why have some stories gripped the imagination of writers, musicians, and artists across cultures and centuries? And what does the emergence and constant re-emergence of such stories tell us about ourselves and others, past and present? What do readers and...
Puzzles about Art and Literature
Both individuals and society attach great importance and value to certain works of art, including poems, novels, films, plays, symphonies, and paintings. Most of us spend a considerable amount of our limited time and resources acquiring, creating, experie...
Reading Culture
This introductory course will give you an overview of the history of literary and cultural studies, and to make you aware of a range of different approaches to cultural texts.
Reading the City
This module will introduce you to studying questions of history, society and culture through the prism of Southampton in order that you can apply those approaches to the study of cities in the French-, Spanish- and German-speaking world.
The module asks big questions. What do we do when we interpret literature and culture, and how can we analyse our practices of interpretation? Can anything be a text, and if so what do we understand by 'literature'? How does literature shape our identity,...
World Dramas
In this module, you will learn how to approach dramatic texts in a way that takes into consideration their place in the world as a complex political, economic, and cultural network. We will focus on questions such as: • What is the difference between r...
Managing Research and Learning
The module will clarify the links between the Year Abroad project and modules in years two and four.
Aesthetics and the Philosophy of Art
You might watch a stunning film, hear a delightful song, enjoy a beautiful sunset, read a dreadful poem, attend an elegant dance, or see a garish building. Experiences like this can stimulate thoughts and feelings of great depth, and provide pleasure or d...
Africa has produced some of the world's outstanding literary texts, yet its literatures, cultures and people are often placed in opposition to the rest of the world. The module engages with the literary fictions by and about Africans, in order to ask: how...
Arthurian Worlds
The figures of King Arthur, Guinevere, his knights and court have exercised a powerful hold over the minds of readers for many centuries. But have you ever wondered about where this legend came from, how it developed, and about the enduring nature of its ...
Before Brexit: Dreams, Nightmares and Ideas of Europe
Britain's recent departure from the European Union has provoked a range of responses, raising urgent questions about our past and future relationship with our neighbours on the Continent. Such questions are not new. From a literary perspective, they promp...
Brief Encounters: Writing Short Stories
Many writers begin with the short story. Through writing short stories they are able to experiment, learn the fundamentals of narrative composition, and have the satisfaction of completing something to a high standard in a relatively short period of time....
Children's literature is a rather slippery term encompassing a variety of genres, child/adult concerns, engagement with historical/contextual issues on, for example, gender; class; nonsense; the nature of time; slavery. Other issues addressed are subject...
Culture, Power and Resistance in the Portuguese-Speaking World
This course is designed to expand and deepen students' knowledge of the cultures of the Portuguese-speaking world, bringing together written texts, visual and conceptual art, political materials, and cinema from twentieth-century Portugal, Brazil, and Lus...
Decolonising Modernity
Literary history is often told in epochs. In particular, it can be useful to understand the world in relation to some or other idea of "modernity": for example, English literary studies is often organised through conceptions of the early modern, the mode...
This course highlights and analyses the link between language structure and its situation of occurrence.
Ethnography of Latin America
This module uses ethnographic approaches to understand the diversity of Latin America's peoples and cultures. Emphasizing the emergence within Latin American anthropology of focuses on everyday life through topics such as kinship and family, ritual and re...
Exploring Spanish Linguistics
The unit introduces you to relevant issues of contemporary Spanish linguistics and establishes the basis for future application of linguistic principles.
From Black and White to Colour: A Screen History of Race, Gender and Sexuality in Post-War Britain
This module presents a history of post-war multicultural Britain through the lens of British film and television, considering how our attitudes to 'race', sexuality and British identity more generally have been defined, challenged and changed by film and...
The course examines major turning points in Spanish and Portuguese America from the middle nineteenth century to the present, with a focus on how these upheavals affected and reflected the politics of class, gender and race.
Globalisation: Culture, Language and The Nation State
This module will problematize the concept of globalisation and explore and develop an understanding of its meaning in economic, political and cultural terms.
Great Writers Steal: Creative Writing and Critical Thinking
Many writers have penned essays about fiction and memoir: E.M. Forster, Virginia Woolf, Henry James, Edith Wharton, Italo Calvino, Vladimir Nabokov, Milan Kundera, A.L. Kennedy, A.S. Byatt, to name just a famous few. Indeed, it seems essential at some p...
High, Popular and Mass Culture in Modern Spain
This course will examine high, popular and mass cultural forms in twentieth century Spain and Latin America. It will discuss notions of mass reproduction and its cultural consequences for cultural form and audience response, including the appropriation of...
Introduction to Nineteenth-Century British Literature
In 1831 the philosopher John Stuart Mill struggled to define the 'Spirit' of the nineteenth century. 'It is', he wrote, 'an age of transition. Mankind have outgrown old institutions and old doctrines, and have not yet acquired new ones.' If the nineteenth...
Learning about Culture: Introduction to Ethnography
Moderns to Contemporaries
What does it mean to make literature new? How do we describe writing now? In this module you will explore the transformations, revolutions, and innovations that have taken place in literature in English when writers have grappled with these questions acr...
This module will introduce you to the notion of 'Multilingualism', how this is understood and represented in different ways, and why it matters to you. You will explore how people become multilingual, and whether it makes a difference if multilinguals are...
This course examines three areas of psycholinguistics which help to understand what the relationship between language and the human mind might be.
Queens, Devils and Players in Early Modern England
Early modern England is a period associated with Elizabeth I and the Tudor court, the plays of Shakespeare, blood and violence on the Jacobean stage, the discovery of new worlds, and the persecution of witches and heretics. The diversity and vitality of t...
Rakes to Romantics
Sound and Voice
This course builds on the basic concepts of phonetics introduced in the first year, with an introduction to acoustic science for the study of speech sounds.
Speech Acts
How do writers activate and amplify the sonic properties of language? Why do artists use vocal performance of text in video art? How can text 'perform' on the page (or onscreen), and what does it mean for language to be performative? What does writing for...
Sweatshops, Sex workers, and Asylum Seekers: World Literature and Visual Culture after Globalisation
What can the voices and narratives of sex workers and asylum seekers depicted in world literature and visual culture tell us about the conditions and pressures of life in the contemporary world? How might considerations of narrative technique, genre, and ...
Syntax: Studying Language Structure
This course will provide you with an introduction to syntax within current linguistic theory.
This unit will introduce you to key issues, concepts and methods in teaching English as a second/foreign language.
The course seeks to provide an overview of the evolution of the European Union (EU) from its early stages to the present. In so doing, it examines the ideas and history of the EU, the institutions of the EU, examples of specific issue areas and the presen...
The Early Modern Body
In this module, students will explore a wealth of different texts and different discourses, from the literary to the scientific, on humanity and the human body in the early modern period. Starting with a glimpse of ancient and modern visions of the body, ...
The Life and Afterlife of the Vikings
Blood, violence, terror, raids, pirates, rape and pillage are just some of the words associated with the Vikings in both the medieval and modern imagination. Their fearsome reputation is underlined by nicknames such as 'Blood Axe' and 'Skull-splitter', bu...
Variation and Change in English
This module takes an empirical approach to questions such as: - Are there patterns of speech and language associated with males and females in varieties of English? - What is the role of teenagers in the propagation of change in English? - After a...
Victorian Feelings
Joy, dejection, devotion, boredom—among the ways in which we respond to literary texts, feelings are perhaps the most immediate and the most permanent. And yet, feeling is often treated as reason's less reputable cousin. For the Victorians, however, feeli...
Vienna and Berlin: Society, Politics and Culture from 1890 to the Present
This module will introduce you to German metropolitan culture and politics in the 20th century with particular reference to Vienna and Berlin, using a wide range of sources which will include literature, film and architecture.
You must study the following module in year 3:
Year Abroad Research Project YARP
The YEAR Abroad Research Project is a 6000 word piece of independent academic writing which you complete in the target language during your residence abroad (or during the summer between your second and final year, in case of exemption from the Year Abroa...
English Dissertation
Undertaking independent research into an aspect of literature or creative writing which particularly interests you is a cornerstone of your degree. A dissertation gives you the opportunity to study a subject in much greater depth than usual and, with gui...
Modern Languages Dissertation
This unit will allow students to undertake independent research to produce an in-depth study of a specific topic located in one of the fields within Modern Languages.
The aim of every language course at the University is to enable you to communicate in your target language at that particular level and in your particular area of interest. We use the word 'communicate' in its widest sense, meaning that you will not only ...
American Dreams? Monetized Bodies, Terror, and Trauma in American Drama
What constitutes the experience of being American, or of America itself? America has been referred to as simultaneously a colony and a colonizer; the first democracy thus representing one of the first populist and anti-colonialist revolutions (1776), but...
As the Puritan colonialist John Winthrop said at Holyrood Church in Southampton before embarking for Boston, American was to be 'as a city upon a hill', a beacon of progress and enlightenment for the world. But from the beginning, America has been shadowe...
Animal Forms: poetry and the non-human
What can animals teach us about the human and non-human? What do the creative forms we use to describe them show us about human form and the other? In this module, you will read a range of poetic and critical material which explores the porous boundaries ...
Audiovisual Translation
This module will introduce you to the different types of audiovisual translation and the various kinds of subtitles produced nowadays. You will learn about the interaction between text and image and the technical issues and constraints involved in creatin...
Barrios and Borders: Language and Identity amongst US Latinos
The module will introduce the main theoretical ideas of language and identity alongside tracing the historical, social and linguistic background to the presence of the so-called Latinos in the US. Issues of language policies in general and those affectin...
Creative Writing in Schools
Are you interested in helping young people study English? This module will introduce you to teaching creative writing in secondary schools by providing training in effective classroom management and guidance on designing lesson plans for studying fiction ...
Encounters with Bodies in Lusophone Cultural Narrative
Based on literary texts, films and visual materials from and about Portugal, Brazil, Angola, Cape Verde, Guinea-Bissau and Mozambique, this course is intended to reflect the cutting edge of Lusophone cultural production and Lusophone Studies research, whi...
English as a Global Language
This module explores the rise of English as a global language focusing on the factors that have led to, and the issues that have arisen from, its dominant status. You will learn about the interrelation between globalisation, standardisation and variabilit...
Exiles, Migrants and Citizens: Narrating and documenting displacement in contemporary Spain
This unit approaches the study of migration and displacement as recurrent themes in Spanish social, political and cultural history since its emergence as a modern nation in 1492, an event itself inaugurated by three major population movements: internal re...
Fantasy Film and Fiction
Fantasy film and fiction spans a wide range of texts, from Gothic 'classics' and feminist fairy tales, to Utopian literature and musicals. Analysing fantasy texts alongside psychoanalytic and cultural theories will enable you to engage with questions conc...
German-Jewish Writing Across the Twentieth Century
The turbulent history of Austrian and German Jews during the twentieth century was accompanied by the production of a diverse and influential body of German-language literature by Jewish authors. Prior to World War Two, Jews played a crucial role in the c...
Historical Memory in Modern Latin America
Holocaust Literature
How has the Holocaust been represented? We will examine a range of responses to the Holocaust from the 1940s to the present day, including memoirs of camp survivors and experimental texts. Focusing on the limits of representation we will approach question...
This new module studies writing and visual representation in the early years of the republic of the United States. Focusing on the period from shortly before the American Revolution to the early years of the nineteenth century, this module will introduce ...
Language Teaching Theory and Practice
This unit examines the theory and practice of language teaching and explores 'reflective practice' as a set of skills that can be applied to your future working life.
Language Testing and Assessment in Society
This module develops awareness of how language testing and assessment have developed in educational and wider social contexts. It focusses on both purposes and processes of language testing and assessment, and critically examines applications in policy ar...
Language and the City
One of the socially and culturally most significant consequences of transnational mobility is that urban populations in particular are increasingly multilingual: in global cities such as London, New York and Berlin there are speakers of hundreds of differ...
Love and Death in Africa's Cities
The stereotype of Africa as a predominantly 'natural' space ignores the existence of large and cosmopolitan urban environments on the continent. Yet today, the sprawling conurbations of Lagos, Nairobi and Johannesburg (as well as Africa's other towns and ...
Minorities and Migrants: Exploring Multicultural Germany
Germany has had a long tradition of immigration and is one of the most multi-cultural countries in Europe today. We will examine the impact of diverse immigration movements on recent German history and notions of German identity. This includes examining b...
Monsters and Others in Medieval Literature and Culture
Monsters lurk at the edges of the medieval map and imagination. These creatures repulse, fascinate, disconcert, and challenge humans in many of medieval Europe's most intriguing and compelling texts from Beowulf to Sir Gawain and the Green Knight. This mo...
Public Service Interpreting
This module will provide students with both a practical and theoretical insight into the role of a Public Service Interpreter. Beginning with a general introduction to interpreting, it will go on to focus more in depth on the wide range of issues and chal...
Radical England: Literature and Crisis in the Seventeenth Century
The seventeenth century was a time of extreme change and political instability in England. In 1649, after years of civil war, Charles I, the King of England, was beheaded on Whitehall in front of a crowd of thousands. England, overnight, became a republic...
Revolution and Romanticism: Literature of the 1790s
The 1790s was a decade of revolutions abroad and of chaos and state paranoia at home. Britain began its longest continuous war in 1792. In a letter years afterwards to Byron, Percy Shelley declared that the French Revolution was 'the master theme of the e...
Sex, Soap Operas and Female Dissidents: Representations of Women in the Hispanic World
This course will introduce you to a range of examples of Spanish American (e.g. Puerto Rican, Argentinean, and Mexican [American]) and Iberian cultural production from the period of the 1980s to the 21st century, in order to provide a sense of the variet...
Shakespeare Then and Now
Has Shakespeare aged well? From the boys in wigs on the Elizabethan stage to the digital wizardry of the twenty-first century, the technology as well as the ideology that informs Shakespearean performance keeps evolving—sometimes in unexpected ways. This ...
Sociophonetic Project Module
This final year module builds on the theoretical grounding students gained in LING 2011 Variation and Change in English and the instrumental analysis techniques from LING 2008 Sound and Voice. In Sociophonetic Project Module, students will put the theory ...
The Origins of Climate Crisis: Ecology in Victorian Literature
Are we living in an age of climate change or climate crisis? In her 2019 speech to the World Economic Forum, Greta Thunberg famously declared "Our house is on fire": a statement underscored by the Australian bushfire crisis of 2020 and the mass devastatio...
Translation plays a major role in the exchange and circulation of practical information and culture production. This means that even if they do not enter the translation profession, in a society that is increasingly global, Modern Linguists are frequently...
Utopias and Dystopias in Literature and Culture
From Plato's Republic and Thomas More's Utopia to Margaret Atwood's Handmaid's Tale and Philip Roth's The Plot Against America, utopias have always been haunted by the spectre of the dystopian. If utopias imagine alternative ways of organizing society, dy...
Writing Queerness
Once upon a time, no one called themselves queer; now it names everything from a kind of person to a type of weather. Queerness seems necessary, ubiquitous, paradoxical – but why? Ranging from the eighteenth century to the present day, this module will ex...
Writing in a Second Language
The unit will take you through the process, the product and the place of writing. Process will deal primarily with modelling cognitive operations, analysis of composing strategies, and individual differences and changes in processes over time. Product wil...
Writing the Novel
The essential elements of writing a novel include crafting beginnings and endings, constructing characters, manipulating structure and plot, and developing an intimate relationship with language. Writing exercises and discussions of work in progress will ...
Course structure Learning and assessment
Learning and assessment
The learning activities for this course include the following:
individual and group projects
independent learning (studying on your own)
How you'll spend your course time:
Your scheduled learning, teaching and independent study for year 1:
Scheduled learning & teaching
How we'll assess you
module journals
written exams
Your assessment breakdown
Year 1:
Practical exam
You'll be supported by a personal academic tutor and have access to a senior tutor.
Elizabeth Hammond is the course leader.
Modules Careers
All employers value the ability to use English accurately and persuasively. When you study English and Spanish at Southampton gives you a strong foundation in:
You'll learn how to tell a story - a crucial skill whether you want to write a press release or funding application, or edit a book or podcast.
The year spent abroad will show employers that you're independent, curious and resourceful. Spanish has over 326 million native speakers and is highly sought after by employers.
This degree can open the door to many careers, including:
Your personal academic tutor can write a reference, based on knowledge of you as a student over the 3 years.
Careers services at Southampton
We are a top 20 UK university for employability (QS Graduate Employability Rankings 2019). Our Careers and Employability Service will support you throughout your time as a student and for up to 5 years after graduation. This support includes:
work experience schemes
CV and interview skills and workshops
careers fairs attended by top employers
a wealth of volunteering opportunities
study abroad and summer school opportunities
We have a vibrant entrepreneurship culture and our dedicated start-up supporter, Futureworlds, is open to every student.
Work in industry
You can take work placements through our Excel internship scheme or Year in Employment scheme. Placements may include those in art galleries, publishing houses, schools and performing arts organisations. We can help you get placements and employment with local, national and international employers.
Learning and assessment Fees, costs and funding
Fees, costs and funding
Fees for a year's study:
UK students pay £9,250.
EU and international students pay £19,300.
What your fees pay for
Your tuition fees pay for the full cost of tuition and all examinations.
Find out how to:
pay your tuition fees
calculate your student finances
Accommodation and living costs, such as travel and food, are not included in your tuition fees. Explore:
accommodation costs
budgeting advice
Bursaries, scholarships and other funding
If you're a UK or EU student and your household income is under £25,000 a year, you may be able to get a University of Southampton bursary to help with your living costs. Find out about bursaries and other funding we offer at Southampton.
If you're a care leaver or estranged from your parents, you may be able to get a specific bursary.
Get in touch for advice about student money matters.
You may be able to get a scholarship or grant that's linked to your chosen subject area.
We award scholarships and grants for travel, academic excellence, or to students from underrepresented backgrounds.
Support during your course
The Student Services Centre offers support and advice on money to students. You may be able to access our Student Support fund and other sources of financial support during your course.
Funding for EU and international students
Find out about funding you could get as an international student.
Careers How to apply
When you apply use:
UCAS course code: QR34
UCAS institution code: S27
Apply for 2022 entry
What happens after you apply?
We will assess your application on the strength of your:
predicted grades
academic reference
We aim to respond to you within 2 to 6 weeks with a decision about your application.
We treat and select everyone in line with our Equality and Diversity Statement.
Fees, costs and funding Related courses
Typical offer: AAB
UCAS course code: Q300
English and French
English and German
English and History
UCAS course code: QV31
English and History with Year Abroad
English and Music
UCAS course code: QW33
English and Music with Year Abroad
English Language and Linguistics
Typical offer: ABB
English Literature, Language and Linguistics with Year Abroad
English with Creative Writing
UCAS course code: CW01
English with Year Abroad
Film and English
Film and English with Year Abroad
Film and Spanish
UCAS course code: RW46
Mathematics with Spanish
Typical offer: AAA
UCAS course code: G1R4
UCAS course code: R990
MLang
Modern Languages (French and Spanish)
UCAS course code: R14R
UCAS course code: R1R4
Modern Languages (French and Spanish) and Linguistics
Modern Languages (French and Spanish) Linguistics
Modern Languages (French, German and Spanish)
Modern Languages (French, Spanish and Chinese)
UCAS course code: R14T
Modern Languages (French, Spanish and Portuguese)
Modern Languages (German and Spanish)
Modern Languages (German and Spanish) and Linguistics
Modern Languages (German and Spanish) Linguistics
Modern Languages (German, Spanish and Chinese)
Modern Languages (German, Spanish and Portuguese)
Modern Languages (Spanish and Portuguese)
Modern Languages (Spanish)
Modern Languages (Spanish) and Business Management
UCAS course code: R4N1
Modern Languages (Spanish) and Linguistics
Modern Languages (Spanish) and Politics
UCAS course code: R42L
Modern Languages (Spanish, Portuguese and Chinese)
Philosophy and English
Philosophy and English with Year Abroad
Spanish and History
UCAS course code: RV41
Spanish and Latin American Studies
UCAS course code: 1G1S
UCAS course code: RTK7


Carolina Software welcomes new WasteWORKS customer, City of Minot, ND. The City converted to WasteWORKS-SQL in November and is enjoying the new functionality and administrative tools with the new system.
Minot is located in north central North Dakota and is the fourth largest city in the state. There are 47,000 residents in Minot, and the Minot Air Force Base is home to the 5th Bomb Wing and 91st Missile Wing, both of the Global Strike Command. Way back in 1886 when railway construction halted for the winter, Minot was the end of the line for the Great Northern Railway. As a result, a tent town sprung up overnight. As if by "magic", the city came to be known as the Magic City, and in the next five months, the population increased to over 5,000 residents, further adding to the nickname's validity.
The City of Minot Landfill is the largest regional waste facility serving six counties in North Dakota. The facility processes approximately 82,000 tons of MSW and 68,800 tons of Inert annually. The Landfill recycles materials such as trees into wood chips and compost. Tires are removed from location and taken to a facility to be ground down and appliances are compacted to be recycled. Residents are also allowed to cut trees brought in to use as firewood, free of charge.
In June 2011, the Mouse River flood destroyed hundreds of homes in Minot and the surrounding area. This unfortunate event led to a dramatic increase in traffic and volume into the landfill. Also during this time, the city began to grow rapidly due to the oil discovery in the region and is still expanding today. New homes, residents, and businesses have added to the already busy landfill. The current daily ticket count is approximately 250.
The WasteWORKS team has made the transition from the 1994 software to their software effortless. They were able to easily setup a training computer with all the waste code, vehicles and accounts for the staff to become accustomed with before going live at the scale. Having the advantage of training with the software beforehand made it possible to customize the program to our specific requirements. The software is extremely flexible with our ever changing needs.