On Shannon entropies in μ-deformed Segal-Bargmann analysis

Pita-Ruiz, Claudio; Sontz, Stephen Bruce

doi:10.1063/1.2178583

On Shannon entropies in μ-deformed Segal-Bargmann analysis

Journal

Journal of Mathematical Physics

ISSN

0022-2488

1089-7658

Date Issued

2006

Author(s)

Pita-Ruiz, Claudio

Facultad de Ingeniería - CampCM

Sontz, Stephen Bruce

Type

text::journal::journal article

DOI

10.1063/1.2178583

URL

https://scripta.up.edu.mx/handle/20.500.12552/3725

Abstract

We consider a deformation of the Segal-Bargmann transform, which is a unitary map from a deformed quantum configuration space onto a deformed quantum phase space (the deformed Segal-Bargmann space). Both of these Hilbert spaces have canonical orthonormal bases. We obtain explicit formulas for the Shannon entropy of some of the elements of these bases. We also consider two reverse log-Sobolev inequalities in the deformed Segal-Bargmann space, which have been proved in a previous work, and show that a certain known coefficient in them is the best possible.