Sworup Kumar Das† , Namita Das‡
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
†sworup.math@gmail.com, P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar-751004, Odisha, India
‡namitadas440@yahoo.co.in, P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar-751004, Odisha, India
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 16 no 2, 2024
