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 ƒ : D → C, the Berezin transform of ƒ is a new function Bƒ : D → C defined at a point z ∈ D by

: $(B f)(z) = \int_D \frac{(1 - |z|^2)^2}{| 1 - z \bar{w} |^4} f(w) \, \mathrm{d}A (w),$

where {{overline|w}} denotes the complex conjugate of w and $\mathrm{d}A$ is the area measure. It is named after Felix Alexandrovich Berezin.

References

{{cite book

| last = Hedenmalm

| 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

| mr = 1758653

}}

External links

{{MathWorld|urlname=BerezinTransform|title=Berezin transform}}

Category:Complex analysis

Category:Operator theory