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 f : D  C, the Berezin transform of f is a new function Bf : D  C defined at a point z  D by

(B f)(z) = \int_{D} \frac{(1 - | z |^{2})^{2}}{| 1 - z \bar{w} |^{4}} f(w) \, \mathrm{dA} (w),

where w denotes the complex conjugate of w and dA is the area measure. It is named after Felix Alexandrovich Berezin.

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