Coherent states quantization of generalized bergman spaces on the unit ball of cn with a new formula for their associated berezin transforms

TL;DR

This paper develops a coherent states quantization approach for generalized Bergman spaces on the unit ball, deriving new formulas for their Berezin transforms expressed via Wilson polynomials and the Laplace-Beltrami operator.

Contribution

It introduces a novel coherent states construction for these spaces and provides an explicit formula for Berezin transforms using Wilson polynomials and Fourier-Helgason transform.

Findings

New coherent states for generalized Bergman spaces

Explicit Berezin transform formulas involving Wilson polynomials

Representation of transforms via Laplace-Beltrami operator

Abstract

While dealing with a class of generalized Bergman spaces on the unit ball, we construct for each of these spaces a set of coherent states to apply a coherent states quantization method. This provides us with another way to recover the Berezin transforms attached to these spaces. Finally, a new formula representing these transforms a functions of the Laplace-Beltrami operator is established in terms ofWilson polynomials by using the Fourier-Helgason transform.