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

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