On Hirschman and log-Sobolev inequalities in mu-deformed Segal-Bargmann analysis

TL;DR

This paper explores a deformed Segal-Bargmann space, analyzing its transform's properties and establishing generalized entropy-entropy and entropy-energy inequalities, extending classical results to the deformed setting.

Contribution

It introduces a deformation of Segal-Bargmann space and derives new entropy and log-Sobolev inequalities within this framework.

Findings

Generalized Hirschman entropy inequalities

Extended log-Sobolev inequalities

Analysis of L^p properties of the deformed transform

Abstract

We consider a deformation of Segal-Bargmann space and its transform. We study L^p properties of this transform and obtain entropy-entropy inequalities (Hirschman) and entropy-energy inequalities (log-Sobolev) that generalize the corresponding known results in the undeformed theory.