Coherent state transforms attached to generalized Bargmann spaces on the complex plane

TL;DR

This paper introduces a new family of coherent states transforms related to generalized Bargmann spaces, providing an alternative method to derive kernels of isometric operators connecting real-line functions with poly-Fock spaces.

Contribution

It constructs a novel family of coherent states transforms associated with generalized Bargmann spaces, expanding the tools for analysis in complex and quantum spaces.

Findings

New coherent states transforms linked to generalized Bargmann spaces.

Alternative derivation of kernels for isometric operators.

Enhanced understanding of connections between real functions and poly-Fock spaces.

Abstract

We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the space of square integrable functions on the real line with the true-poly-Fock spaces [Oper.Theory. Adv.Appl.,v.117,2000].