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Densities and differentiability properties of Gauss semigroups on a Lie group

Author: Eberhard Siebert
Journal: Proc. Amer. Math. Soc. 91 (1984), 298-305
MSC: Primary 60B15; Secondary 43A05, 47D05
MathSciNet review: 740190
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Abstract: We consider an absolutely continuous Gauss semigroup on a connected Lie group. Integrability and boundedness properties for the corresponding densities are established. Moreover it is shown that the Gauss measures transform integrable functions into infinitely differentiable solutions of certain partial differential equations. Finally, we prove that the semigroup acts on many Banach spaces as a differentiable operator semigroup.

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Keywords: Gauss semigroup, connected Lie group, absolute continuity, hypoelliptic differential operator, weakly sequentially complete Banach space, differentiable operator semigroup
Article copyright: © Copyright 1984 American Mathematical Society

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