title: Berezin transform
text: # Berezin transform
  
  In mathematics — specifically, in complex analysis — the Berezin transform is an integral operator acting on functions defined on the open unit disk D of the complex plane C. Formally, for a function ƒ : D → C, the Berezin transform of ƒ is a new function Bƒ : D → C defined at a point z ∈ D by
  
      $(Bf)(z)=\int _{D}{\frac {(1-|z|^{2})^{2}}{|1-z{\bar {w}}|^{4}}}f(w)\,\mathrm {d} A(w),$
  
  where w denotes the complex conjugate of w and $\mathrm {d} A$ is the area measure. It is named after Felix Alexandrovich Berezin.
  
  