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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hypercontractivity estimates for nonselfadjoint diffusion semigroups


Author: Ross Pinsky
Journal: Proc. Amer. Math. Soc. 104 (1988), 532-536
MSC: Primary 60J60; Secondary 47D05, 60J30
MathSciNet review: 962824
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Abstract: We use Gross' results on logarithmic Sobolev inequalities and hypercontractivity to show that the hypercontractivity of a positive recurrent diffusion semigroup depends essentially only on its invariant probability measure and a given diffusion matrix and its diffusion matrix. Thus all diffusion semigroups (including the unique selfadjoint one) with a given invariant probability measure and a given diffusion matrix are essentially equally hypercontractive.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0962824-6
PII: S 0002-9939(1988)0962824-6
Keywords: Hypercontractivity, logarithmic Sobolev inequalities, nonselfadjoint elliptic operator, diffusion semigroup
Article copyright: © Copyright 1988 American Mathematical Society