Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space

We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant. To do this, we use the notion of entropy. We also give an example of a...

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Autor principal: Shigekawa, Ichiro
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512736/
https://www.ncbi.nlm.nih.gov/pubmed/33265311
http://dx.doi.org/10.3390/e20040220
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author Shigekawa, Ichiro
author_facet Shigekawa, Ichiro
author_sort Shigekawa, Ichiro
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description We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant. To do this, we use the notion of entropy. We also give an example of a Laguerre operator. We determine the spectrum in the Orlicz space and discuss the relation between the logarithmic Sobolev constant and the spectral gap.
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spelling pubmed-75127362020-11-09 Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space Shigekawa, Ichiro Entropy (Basel) Article We investigate the exponential convergence of a Markovian semigroup in the Zygmund space under the assumption of logarithmic Sobolev inequality. We show that the convergence rate is greater than the logarithmic Sobolev constant. To do this, we use the notion of entropy. We also give an example of a Laguerre operator. We determine the spectrum in the Orlicz space and discuss the relation between the logarithmic Sobolev constant and the spectral gap. MDPI 2018-03-23 /pmc/articles/PMC7512736/ /pubmed/33265311 http://dx.doi.org/10.3390/e20040220 Text en © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Shigekawa, Ichiro
Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space
title Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space
title_full Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space
title_fullStr Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space
title_full_unstemmed Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space
title_short Logarithmic Sobolev Inequality and Exponential Convergence of a Markovian Semigroup in the Zygmund Space
title_sort logarithmic sobolev inequality and exponential convergence of a markovian semigroup in the zygmund space
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512736/
https://www.ncbi.nlm.nih.gov/pubmed/33265311
http://dx.doi.org/10.3390/e20040220
work_keys_str_mv AT shigekawaichiro logarithmicsobolevinequalityandexponentialconvergenceofamarkoviansemigroupinthezygmundspace

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