Hypergroups and the Markov Sequence Problem

Monday, April 27, 2015 - 9:30am - 10:20am
Keller 3-180
Dominique Bakry (Université de Toulouse III (Paul Sabatier))
Given an orthonormal basis for the L2 space of some probability space, one wants to describe all Markov kernels for which the elements of the basis are eigenvectors. The hypergroup property is a property of the basis which allows for such description. The famous Gasper theorem asserts that this property is valid for the family of Jacobi polynomials in dimension 1. A recent proof of this by Carlen-, Geronimo and Loss provides a way to deal with this problem in a more general setting. We shall in particular provide some results for a natural family of orthogonal polynomials on the simplex in any dimension, and also on the family of Heckman-Opdam polynomials associated with the A2 and G2 root systems in the plane.
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