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Analytische Vektoren von Faltungshalbgruppen II. Funktionenräume, auf lokalkompakten Gruppen

Analytical vectors of convolution semigroups II. Function spaces on locally compact groups

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Abstract

In this paper the investigations of [3], [4], [5] are continued. LetG be a locally compact group. First we show that in general there is no rich subspace of functions of the Bruhat-spaceD (G), whose, elements are analytical vectors for any convolution semigroup of probability measures. On the other hand we are able to construct dense subspaces ofC 0 (G) of analytical vectors, ifG is a Moore-group or a symmetric Riemannian space. We study properties of these subspaces and their relations to the structure, of the groupG.

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Authors and Affiliations

  1. Abteilung Mathematik, Universität Dortmund, Postfach 500500, D-4600, Dortmund 50, Bundesrepublik Deutschland

    T. Drisch & W. Hazod

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  1. T. Drisch
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  2. W. Hazod
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Herrn Prof. Dr. L. Schmetterer zum 60. Geburtstag gewidmet

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Drisch, T., Hazod, W. Analytische Vektoren von Faltungshalbgruppen II. Funktionenräume, auf lokalkompakten Gruppen. Monatshefte für Mathematik 88, 107–122 (1979). https://doi.org/10.1007/BF01319098

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