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, Volume 72, Issue 1, pp 141–153 | Cite as

On the Fourier transformation of positive, positive definite measures on commutative hypergroups, and dual convolution structures

  • Michael Voit


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\(supp(\delta _\alpha * \delta _{\bar \alpha } )\) contains a positive character for\(\alpha \in \hat K\) whenever a dual convolution exists. In particular, if1supp 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.


Compact Abelian Group Double Coset Positive Character Positive Definite Function Jacobi Function 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Michael Voit
    • 1
  1. 1.Mathematisches Institut Technische Universität MünchenMünchen 2FRG

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