Deformations of convolution semigroups on commutative hypergroups

Details Deformations of convolution semigroups on commutative hypergroups Deformations of convolution semigroups on commutative hypergroups

2004-05-13

arxiv.org/abs/math/0405255v1

Mathematics

Probability

To appear in: Infinite Dimensional Harmonic Analysis; Conf.Proc. Tuebingen 2003; World Scientific, Singapore

Scientific paper

It was recently shown by the authors that deformations of hypergroup convolutions w.r.t. positive semicharacters can be used to explain probabilistic connections between the Gelfand pairs (SL(d,C), SU(d)) and Hermitian matrices. We here study connections between general convolution semigroups on commutative hypergroups and their deformations. We are able to develop a satisfying theory, if the underlying positive semicharacter has some growth property. We present several examples which indicate that this growth condition holds in many interesting cases.

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