Convolution algebras for multivariable Bessel functions

摘要

In this article we give an overview of recent results on hypergroup algebras which are associated with Bessel functions on cones of positive semidefinite matrices and a class of Dunkl-type Bessel functions for root systems of type B. The Bessel hypergroups on matrix cones are obtained from a discrete series with a group-theoretic background by interpolation with respect to a dimension parameter. Passing to the matrix spectra leads to Bessel functions of Dunkl type and three continuous series of hypergroup algebras matching the Dunkl transform in the Weyl-group invariant case.