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

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

where ȳ denotes the complex conjugate of y.

[edit] References

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