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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… Click to show full 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.
Keywords:
space;
sobolev;
convergence markovian;
exponential convergence;
logarithmic sobolev
Journal Title: Entropy
Year Published: 2018
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Journal Title: Entropy
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!