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Title: Reverse inequalities in {mu}-deformed Segal-Bargmann analysis

Abstract

We prove reverse hypercontractivity inequalities as well as reverse log-Sobolev inequalities in the context of a space of holomorphic functions, which is called the {mu}-deformed Segal-Bargmann space and arises in the works of Wigner, Rosenblum, and Marron. To achieve this we define {mu}-deformations of energy and entropy. Our principle results generalize earlier works of Carlen and Sontz. We also show that the semigroup of this theory is L{sup p} bounded, and we conjecture that it is L{sup p} contractive and, even more strongly, that it is hypercontractive.

Authors:
;  [1];  [2]
  1. Universidad Autonoma de San Luis Potosi, San Luis Potosi (Mexico)
  2. (CIMAT), Guanajuato (Mexico)
Publication Date:
OSTI Identifier:
20768760
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 4; Other Information: DOI: 10.1063/1.2186257; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DEFORMATION; ENTROPY; FUNCTIONAL ANALYSIS; FUNCTIONS; GROUP THEORY; MATHEMATICAL SPACE; QUANTUM MECHANICS

Citation Formats

Angulo Aguila, Carlos, Sontz, Stephen Bruce, and Centro de Investigacion en Matematicas, A.C. Reverse inequalities in {mu}-deformed Segal-Bargmann analysis. United States: N. p., 2006. Web. doi:10.1063/1.2186257.
Angulo Aguila, Carlos, Sontz, Stephen Bruce, & Centro de Investigacion en Matematicas, A.C. Reverse inequalities in {mu}-deformed Segal-Bargmann analysis. United States. doi:10.1063/1.2186257.
Angulo Aguila, Carlos, Sontz, Stephen Bruce, and Centro de Investigacion en Matematicas, A.C. Sat . "Reverse inequalities in {mu}-deformed Segal-Bargmann analysis". United States. doi:10.1063/1.2186257.
@article{osti_20768760,
title = {Reverse inequalities in {mu}-deformed Segal-Bargmann analysis},
author = {Angulo Aguila, Carlos and Sontz, Stephen Bruce and Centro de Investigacion en Matematicas, A.C.},
abstractNote = {We prove reverse hypercontractivity inequalities as well as reverse log-Sobolev inequalities in the context of a space of holomorphic functions, which is called the {mu}-deformed Segal-Bargmann space and arises in the works of Wigner, Rosenblum, and Marron. To achieve this we define {mu}-deformations of energy and entropy. Our principle results generalize earlier works of Carlen and Sontz. We also show that the semigroup of this theory is L{sup p} bounded, and we conjecture that it is L{sup p} contractive and, even more strongly, that it is hypercontractive.},
doi = {10.1063/1.2186257},
journal = {Journal of Mathematical Physics},
number = 4,
volume = 47,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}