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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/912| DIRECT AND REVERSE LOG-SOBOLEV INEQUALITIES IN -DEFORMED SEGAL BARGMANN ANALYSIS | |
| STEPHEN BRUCE SONTZ | |
| Acceso Abierto | |
| Atribución-NoComercial-CompartirIgual | |
| Espacios de Banach | |
| Both direct and reverse log-Sobolev inequalities, relating the Shannon entropy with a - deformed energy, are shown to hold in a family of -deformed Segal{Bargmann spaces. This shows that the -deformed energy of a state is nite if and only if its Shannon entropy is nite. The direct inequality is a new result, while the reverse inequality has already been shown by the authors but using dierent methods. Next the -deformed energy of a state is shown to be nite if and only if its Dirichlet form energy is nite. 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 nite if and only if its Shannon entropy is nite. The main method used here is based on a study of the reproducing kernel function of these spaces and the associated integral kernel transform. | |
| World Scientific | |
| 2007 | |
| Artículo | |
| Inglés | |
| Investigadores | |
| OTRAS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Matemáticas |
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| SSontz.pdf | 346.84 kB | Adobe PDF | Visualizar/Abrir |