The aims of these lecture notes are twofold. On the one hand, they are meant as an
introduction to rational and trigonometric Dunkl theory, starting with the historical examples …

This paper surveys eight classes of polynomials associated with $ A $-type and $ BC $-type
root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or …

One‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N
particles can be regarded as diffusion processes on suitable subsets of RN R^N like Weyl …

We continue a program generalizing classical results from the analysis on symmetric cones
to the Dunkl setting for root systems of type $ A $. In particular, we prove a Dunkl-Laplace …

+ 1) 2! is the holomorphic solution of the hypergeometric equation around z= 0 with
exponent 0 and normalized by F (a, b; c; 0)= 1. It is well defined if c− N, is convergent for| z|< …

We present an explicit difference equation for the Heckman–Opdam hypergeometric
function associated with root systems. Via a confluent hypergeometric limit, an analogous …

The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions
in one variable and include the spherical functions of non-compact Grassmann manifolds …

This paper studies the asymptotic behavior of several central objects in Dunkl theory as the
dimension of the underlying space grows large. Our starting point is the observation that a …

We introduce a Cherednik kernel and a hypergeometric function for integral root systems
and prove their relation to spherical functions associated with Riemannian symmetric …

We study analytic properties of a Hankel transform for the type A Dunkl setting with arbitrary
multiplicity parameter k≥ 0 which goes back to Baker and Forrester and, in an earlier …