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

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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Bibliographic Details
Main Author: Ichiro Shigekawa
Format: Article
Language:English
Published: MDPI AG 2018-03-01
Series:Entropy
Subjects:
Dirichlet form
logarithmic Sobolev inequality
entropy
spectrum
Zygmund space
Laguerre operator
Online Access:http://www.mdpi.com/1099-4300/20/4/220

Internet

http://www.mdpi.com/1099-4300/20/4/220

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