A Formula representing magnetic Berezin transforms on the Bergman ball of $\C^n$ as functions of the Laplace-Beltrami operator

TL;DR

This paper derives a formula expressing magnetic Berezin transforms on the Bergman ball as functions of the Laplace-Beltrami operator, extending previous results and providing a new analytical tool for generalized Bergman spaces.

Contribution

The paper introduces a new formula linking magnetic Berezin transforms to the Laplace-Beltrami operator on the Bergman ball, generalizing earlier findings.

Findings

Derived a formula representing Berezin transforms as functions of the Laplace-Beltrami operator

Extended previous results by J. Peeter to generalized Bergman spaces

Provided a new analytical framework for magnetic Berezin transforms

Abstract

We give a formula that represents magnetic Berezin transforms associated with generalized Bergman spaces as functions of the Laplace-Beltrami operator on the Bergman ball. In particular, we recover the result obtained by J. Peeter [J. Oper. Theory, 24, 1990].