What is Functional analysis?
'''Functional analysis''' is a branch of [[mathematical analysis]].<ref>[[Leonid Kantorovich|Kantorovich, L. V.]], & Akilov, G. P. (1982). Functional Analysis Pergamon Press. University of Michigan.</ref><ref>Deimling, K. (2010). Nonlinear functional analysis. Courier Corporation.</ref> This area emerged from the studies of [[differential equations]] (especially [[partial differential equations]]<ref>Brezis, H. (2010). Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer Science & Business Media.</ref>). It has many applications in various fields.<ref>Zeidler, E., Nonlinear Functional Analysis and Its Applications I-V. Springer Science & Business Media.</ref><ref>Zeidler, E. (2012). Applied functional analysis: main principles and their applications. Springer Science & Business Media.</ref><ref>Zeidler, E. (2012). Applied functional analysis: applications to mathematical physics. Springer Science & Business Media.</ref> One of the famous use is [[numerical analysis]].<ref>Collatz, L. (2014). Functional analysis and numerical mathematics. Academic Press</ref><ref>Computational Functional Analysis 2nd Edition, Ramon Moore & Michael Cloud (2007), Woodhead Publishing.</ref><ref>Lebedev, V. I. (2000). Functional analysis and computational mathematics. Moscow: Fizmatlit.</ref><ref> M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).</ref> ==References== {{reflist|2}} ==Further reading== {{columns-list|colwidth=20em| * Aliprantis, C.D., Border, K.C.: ''Infinite Dimensional Analysis: A Hitchhiker's Guide'', 3rd ed., Springer 2007, {{ISBN|978-3-540-32696-0}}. Online {{doi|10.1007/3-540-29587-9}} (by subscription) * Bachman, G., Narici, L.: ''Functional analysis'', Academic Press, 1966. (reprint Dover Publications) * Banach S.: [http://www.ebook3000.com/Theory-of-Linear-Operations--Volume-38--North-Holland-Mathematical-Library--by-S--Banach_134628.html ''Theory of Lin