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

Entropy

Ichiro Shigekawa¹ 

[1] Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan;

关键词: Dirichlet form;    logarithmic Sobolev inequality;    entropy;    spectrum;    Zygmund space;    Laguerre operator;   

DOI  :  10.3390/e20040220

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown