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