Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis
| dc.creator | Aguila, Carlos Ernesto Angulo | |
| dc.creator | Sontz, Stephen Bruce | |
| dc.date | 2007-07-21 | |
| dc.date.accessioned | 2026-07-07T08:19:37Z | |
| dc.date.available | 2026-07-07T08:19:37Z | |
| dc.description | Both direct and reverse log-Sobolev inequalities, relating the Shannon entropy with a $μ$-deformed energy, are shown to hold in a family of $μ$-deformed Segal-Bargmann spaces. This shows that the $μ$-deformed energy of a state is finite if and only if its Shannon entropy is finite. The direct inequality is a new result, while the reverse inequality has already been shown by the authors but using different methods. Next the $μ$-deformed energy of a state is shown to be finite if and only if its Dirichlet form energy is finite. This leads to both direct and reverse log-Sobolev inequalities that relate the Shannon entropy with the Dirichlet energy. We obtain that the Dirichlet energy of a state is finite if and only if its Shannon entropy is finite. The main method used here is based on a study of the reproducing kernel function of these spaces and the associated integral kernel transform. | |
| dc.description | Accepted for publication in Infinite Dimensional Analysis, Quantum Probability and Related Topics | |
| dc.identifier | https://arxiv.org/abs/0707.3227 | |
| dc.identifier | http://arxiv.org/abs/0707.3227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134823 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81S99 | |
| dc.title | Direct and reverse log-Sobolev inequalities in $μ$-deformed Segal-Bargmann analysis | |
| dc.type | text |