Berezin transform

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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 is the area measure. It is named after Felix Alexandrovich Berezin.


  • Hedenmalm, Haakan; Korenblum, Boris; Zhu, Kehe (2000). Theory of Bergman spaces. Graduate Texts in Mathematics. 199. New York: Springer-Verlag. pp. 28–51. ISBN 0-387-98791-6. MR 1758653. 

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