Séminaire OrléansSome aspects of harmonic analysis in Heckman-Opdam theory
Margit Rösler (Universität Paderborn)
Thursday 05 June 2014 14:00 - Orléans - Salle de Séminaire
Heckman-Opdam theory deals with multivariable generalizations of classical hypergeometric functions in one variable, which are well-known to play an important role in the analysis on spheres and hyperbolic spaces. The hypergeometric functions of Heckman and Opdam include the spherical functions of general Riemannian symmetric spaces as particular cases. In this talk, we give an introduction to the basic analytic ingredients of this theory, starting from examples in one variable. We explain the role of differential-reflection operators (called Dunkl operators) in this context, and we address some more recent issues, such as product formulas and limit transitions related to infinite dimensional Grassmann manifolds.