35 citations · 58 across the 12 of their papers we have counts for
14 papers
Dunkl theory, convolution algebras, and related Markov processes
Margit Rösler, Michael Voit
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 exa…
Littlewood-Paley theory for orthogonal expansions associated with root systems
Lukas Langen, Margit Rösler
We introduce the non-symmetric heat and Poisson semigroups associated with the Heckman-Opdam Laplacian in the compact setting. Based on the Poisson semigroup, we study several Litt…
Remarks on a proof of the absolute continuity of the representing measures for Dunkl's intertwining operator
Dominik Brennecken, Margit Rösler
In the published paper [T10], K. Trimèche presented a proof of the statement that for suitable nonnegative multiplicities and regular arguments, the representing measures of Dunkl'…
Limits of Bessel functions for root systems as the rank tends to infinity
Dominik Brennecken, Margit Rösler
We study the asymptotic behaviour of Bessel functions associated of root systems of type and type with positive multiplicities as the rank tends to infinity. In…
Beta distributions and Sonine integrals for Bessel functions on symmetric cones
Margit Rösler, Michael Voit
There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index with respect to such functions of lower index…
On the Green function and Poisson integrals of the Dunkl Laplacian
Piotr Graczyk, Tomasz Luks, Margit Rösler
We prove the existence and study properties of the Green function of the unit ball for the Dunkl Laplacian in . As applications we derive the Poisson-Jensen for…
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
Margit Rösler, Michael Voit
We consider compact Grassmann manifolds over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type . From an explicit…
Integral representation and sharp asymptotic results for some Heckman-Opdam hypergeometric functions of type BC
Margit Rösler, Michael Voit
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 over…
Olshanski spherical functions for infinite dimensional motion groups of fixed rank
Margit Rösler, Michael Voit
Consider the Gelfand pairs associated with motion groups over the fields with and fixed $…
Limit transition between hypergeometric functions of type BC and type A
Margit Rösler, Tom Koornwinder, Michael Voit
Let be the Heckman-Opdam hypergeometric function of type BC with multiplicities and weighted half sum of positive roots. We prove that $F_{…
The heat semigroup in the compact Heckman-Opdam setting and the Segal-Bargmann transform
Heiko Remling, Margit Rösler
In the first part of this paper, we study the heat equation and the heat kernel associated with the Heckman-Opdam Laplacian in the compact, Weyl-group invariant setting. In particu…
Convolution algebras for Heckman-Opdam polynomials derived from compact Grassmannians
Heiko Remling, Margit Rösler
We study convolution algebras associated with Heckman-Opdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroup…
Asymptotic analysis for the Dunkl kernel
Margit Rösler, Marcel de Jeu
This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infi…
Biorthogonal polynomials associated with reflection groups and a formula of Macdonald
Margit Rösler, Michael Voit
Dunkl operators are differential-difference operators on $\b R^N$ which generalize partial derivatives. They lead to generalizations of Laplace operators, Fourier transforms, heat…