Densities and differentiability properties of Gauss semigroups on a Lie group

Siebert, Eberhard

doi:10.1090/S0002-9939-1984-0740190-5

Densities and differentiability properties of Gauss semigroups on a Lie group
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Proc. Amer. Math. Soc. 91 (1984), 298-305 Request permission

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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Holomorphy of convolution semigroups