On the Fourier transformation of positive,positive definite measures on commutative hypergroups,and dual convolution structures |
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Authors: | Michael Voit |
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Institution: | 1. Mathematisches Institut Technische Universit?t München, Arcisstr. 21, D-8000, München 2, FRG
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Abstract: | We show that the support of the Fourier transform of a positive, positive definite measure on a commutative hypergroupK contains a positive character. This generalizes the known fact that the support of the Plancherel measure π contains a positive
character (which in general is not the identity character1). It follows that
contains a positive character for
whenever a dual convolution exists. In particular, if1∈supp π, then1 is this character. We also give some further general results about the support of dual convolution products in terms ofsupp π. Some examples associated with Gelfand pairs and, in particular, non-compact Riemannian symmetric spaces of rank 1 are
discussed. |
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Keywords: | |
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