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 …

We conjecture a geometrical form of the Paley–Wiener theorem for the Dunkl transform and
prove three instances thereof, by using a reduction to the one-dimensional even case, shift …

These lecture notes are intended as an introduction to the theory of rational Dunkl operators,
the associated special functions and related Markov processes with an emphasis on …

Using a polarization of a suitable restriction map, and heat-kernel analysis, we construct a
generalized Segal-Bargmann transform associated with every finite Coxeter group G on ℝ …

In this paper, we extend the iterative expression for the generalized spherical functions
associated with the root systems of type A previously obtained (Sawyer in Trans Am Math …

Let k=(kα) αεℝ, be a positive-real valued multiplicity function related to a root system ℝ, and
Δk be the Dunkl-Laplacian operator. For (x, t) ε ℝN,× ℝ, denote by uk (x, t) the solution to the …

Let A and B be two n× n Hermitian matrices. Assume that the eigenvalues α 1,…, α n of A are
known, as well as the eigenvalues β 1,…, β n of B. What can be said about the eigenvalues …

Abstract We derive Mehler–Heine type asymptotic formulas for Charlier and Meixner
polynomials, and also for their associated families. These formulas provide good …

By taking an appropriate zero-curvature limit, we obtain the spherical functions on flat
symmetric spaces G0/K as limits of the Harish-Chandra's spherical functions. New and …

We study the addition of two random independent $ M\times N $ rectangular random
matrices with invariant distributions in two limit regimes, where the parameter beta (inverse …