Berezin transform

In mathematics &mdash; specifically, in complex analysis &mdash; 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.