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

$(Bf)(z)=\underset{D}{\int }\frac{(1-|z{|}^2{)}^2}{|1-z\overline{w}{|}^4}f(w)\mathrm{d}A(w),$

where w denotes the complex conjugate of w and $\mathrm{d}A$ is the area measure. It is named after Felix Alexandrovich Berezin.

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