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

Journal Article · Sat Apr 15 04:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2186257· OSTI ID:20768760

Angulo Aguila, Carlos; Sontz, Stephen Bruce ^[1]

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1. Universidad Autonoma de San Luis Potosi, San Luis Potosi (Mexico)

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.

• OSTI ID: 20768760
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 4 Vol. 47; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DEFORMATION
ENTROPY
FUNCTIONAL ANALYSIS
FUNCTIONS
GROUP THEORY
MATHEMATICAL SPACE
QUANTUM MECHANICS