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Holomorphicity of a class of semigroups of measures operating on $ L\sp{p}(G/H)$

Author: Tomasz Przebinda
Journal: Proc. Amer. Math. Soc. 87 (1983), 637-643
MSC: Primary 47D05; Secondary 22E30, 43A10
MathSciNet review: 687632
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Abstract: In the present paper we consider the class of stable semigroups of measures on a Lie group $ G$. This class contains the Gaussian semigroups. We prove that under certain strongly continuous representations of $ G$ acting in $ {L^p}(G/H)$, $ 1 \leqslant p < \infty $, these semigroups are holomorphic and uniformly bounded.

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Keywords: Semigroups of measures, holomorphic semigroups, Lie groups, Haar measure, absolutely continuous measures, group representations
Article copyright: © Copyright 1983 American Mathematical Society

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