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 ofC0 (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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