An example in the theory of hypercontractive semigroups

Authors:
Andrzej Korzeniowski and Daniel W. Stroock

Journal:
Proc. Amer. Math. Soc. **94** (1985), 87-90

MSC:
Primary 47D05; Secondary 47B38

MathSciNet review:
781062

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Abstract | References | Similar Articles | Additional Information

Abstract: Let on be the Laguerre operator. It is shown that for , and has norm 1 if and only if and the corresponding logarithmic Sobolev constant is not equal to , where is the smallest nonzero eigenvalue of .

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1985-0781062-0

Keywords:
Laguerre semigroup,
logarithmic Sobolev inequality,
Ornstein-Uhlenbeck semigroup,
hypercontractivity

Article copyright:
© Copyright 1985
American Mathematical Society