A positivity result and normalization of positive convolution structures.
Affine Dunkl processes of type
We introduce the analogue of Dunkl processes in the case of an affine root system of type . The construction of the affine Dunkl process is achieved by a skew-product decomposition by means of its radial part and a jump process on the affine Weyl group, where the radial part of the affine Dunkl process is given by a Gaussian process on the ultraspherical hypergroup . We prove that the affine Dunkl process is a càdlàg Markov process as well as a local martingale, study its jumps, and give a martingale...
Amenability and weak amenability of l¹-algebras of polynomial hypergroups
We investigate amenability and weak amenability of the l¹-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, we prove amenability for the hypergroup induced by the Chebyshev polynomials of the first kind.
An extension of the spectral mapping theorem.