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.
Compact Groups Having Almost Discrete Orbit Hypergroups.
Convolution operators on the dual of hypergroup algebras
Let be a hypergroup. In this paper, we define a locally convex topology on such that with the strong topology can be identified with a Banach subspace of . We prove that if has a Haar measure, then the dual to this subspace is has compact carrier}. Moreover, we study the operators on and which commute with translations and convolutions. We prove, among other things, that if is left stationary, then there is a weakly compact operator on which commutes with convolutions if and...
Duals of subhypergroups and quotients of commutative hypergroups.
Ergodic sequences of probability measures on commutative hypergroups.
Exponential monomials on Sturm-Liouville hypergroups.
Fourier Transforms of Schwartz Functions on Chébli-Trimèche Hypergroups.
Generalized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup
Mathematics Subject Classification: 42B35, 35L35, 35K35In this paper we study generalized Strichartz inequalities for the wave equation on the Laguerre hypergroup using generalized homogeneous Besov-Laguerre type spaces.
Homomorphisms of -algebras on signed polynomial hypergroups.
Induced representations and duality results for commutative hypergroups.
Induced Representations and Hypergroup Homomorphisms.
Induced representations of hypergroups.
Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups
Let K be an ultraspherical hypergroup associated to a locally compact group G and a spherical projector π and let VN(K) denote the dual of the Fourier algebra A(K) corresponding to K. In this note, invariant means on VN(K) are defined and studied. We show that the set of invariant means on VN(K) is nonempty. Also, we prove that, if H is an open subhypergroup of K, then the number of invariant means on VN(H) is equal to the number of invariant means on VN(K). We also show that a unique topological...
Jacobi radial stable processes
Littlewood-Paley -functions and multipliers for the Laguerre hypergroup.
Local Hardy spaces on Chébli-Trimèche hypergroups
We investigate the local Hardy spaces on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.
Moment functions and laws of large numbers on hypergroups.