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- W2170676511 abstract "Both direct and reverse log-Sobolev inequalities, relating the Shannon entropy with a $mu$-deformed energy, are shown to hold in a family of $mu$-deformed Segal-Bargmann spaces. This shows that the $mu$-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 $mu$-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." @default.
- W2170676511 created "2016-06-24" @default.
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- W2170676511 date "2007-07-21" @default.
- W2170676511 modified "2023-09-27" @default.
- W2170676511 title "Direct and reverse log-Sobolev inequalities in $mu$-deformed Segal-Bargmann analysis" @default.
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