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Affine Dunkl processes of type A ˜ 1

François Chapon (2012)

Annales de l'I.H.P. Probabilités et statistiques

We introduce the analogue of Dunkl processes in the case of an affine root system of type A ˜ 1 . 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 [ 0 , 1 ] . 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

Rupert Lasser (2007)

Studia Mathematica

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.

Convolution operators on the dual of hypergroup algebras

Ali Ghaffari (2003)

Commentationes Mathematicae Universitatis Carolinae

Let X be a hypergroup. In this paper, we define a locally convex topology β on L ( X ) such that ( L ( X ) , β ) * with the strong topology can be identified with a Banach subspace of L ( X ) * . We prove that if X has a Haar measure, then the dual to this subspace is L C ( X ) * * = cl { F L ( X ) * * ; F has compact carrier}. Moreover, we study the operators on L ( X ) * and L 0 ( X ) which commute with translations and convolutions. We prove, among other things, that if wap ( L ( X ) ) is left stationary, then there is a weakly compact operator T on L ( X ) * which commutes with convolutions if and...

Invariant means on a class of von Neumann algebras related to ultraspherical hypergroups

Nageswaran Shravan Kumar (2014)

Studia Mathematica

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...

Local Hardy spaces on Chébli-Trimèche hypergroups

Walter Bloom, Zengfu Xu (1999)

Studia Mathematica

We investigate the local Hardy spaces h p on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.

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