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Title: Logarithmic Sobolev inequality and exponential convergence of a Markovian semigroup in the Zygmund space
Authors: Shigekawa, Ichiro  kyouindb  KAKEN_id
Author's alias: 重川, 一郎
Keywords: Dirichlet form
logarithmic Sobolev inequality
entropy
spectrum
Zygmund space
Laguerre operator
Issue Date: 23-Mar-2018
Publisher: MDPI AG
Journal title: Entropy
Volume: 20
Issue: 4
Thesis number: 220
Abstract: 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.
Rights: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
URI: http://hdl.handle.net/2433/234179
DOI(Published Version): 10.3390/e20040220
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