Berezin transform

Berezin transform

In mathematics — specifically, in complex analysis — the Berezin transform, named after Felix Alexandrovich Berezin, 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 ar{y} |^{4 f(z) , mathrm{d} y,

where "ȳ" denotes the complex conjugate of "y".

References

* cite book
last = Hedenmalm
first = Haakan
coauthors = Korenblum, Boris and Zhu, Kehe
title = Theory of Bergman spaces
series= Graduate Texts in Mathematics | volume=199
publisher = Springer-Verlag
location = New York
year = 2000
pages = 28–51
isbn = 0-387-98791-6 MathSciNet|id=1758653

External links

*


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