THE BEREZIN TRANSFORMATION ON L2(U+)*

Sworup Kumar Das Namita Das

Dedicated to Dr. Dan Tiba on the occasion of his 70th anniversary

 

Abstract

Let) be the Bergman space of the upper half plane U+.

In this paper, we consider the integral operator H from L2(U+) into Z

L2(U+) defined by (Hf)(w) = fe(w) =                                f(s)|dw(s)|2dAe(s),w ∈ U+,

U+

where and dAe is the area measure on

U+. We refer the map H as the Berezin transformation defined on L2(U+). We have derived various algebraic properties of the operator and showed that considered as an operator on L2a(U+).

Keywords: Bergman space, upper half plane, integral operators, Berezin transformation, reproducing kernel.

MSC: 47B38, 30H20, 45P05.

DOI https://doi.org/10.56082/annalsarscimath.2024.2.162

Abstract Article                                                                                  Volume 16 no 2 / 2024