Mathematische Gesellschaft am 19.12.2013
Donnerstag, 19.12.2013, 16.45 Uhr, Sitzungszimmer
Margit Rösler, Paderborn
"Heckman-Opdam hypergeometric functions and harmonic analysis"
Classical hypergeometric functions such as Gegenbauer polynomials and
the Gaussian hypergeometric function are known to
play an important role in the analysis on spheres and hyperbolic spaces.
There are multivariable generalizations of
such functions within a theory of Heckman, Opdam
and Cherednik, which in particular include the
spherical functions of general Riemannian symmetric spaces.
In this talk, we give an overview of the basic ingredients in the theory
of such hypergeometric functions and the harmonic analysis associated
starting from examples in one variable. We explain the role of
(called Dunkl operators) in this theory, and we
address some more recent issues, such as limit transitions
related to infinite dimensional Grassmann manifolds.