Margit Rösler
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Multiresolution analysis on spectra of hermitian matrices Open
We establish a multiresolution analysis on the space $\text{Herm}(n)$ of $n\times n$ complex Hermitian matrices which is adapted to invariance under conjugation by the unitary group $U(n).$ The orbits under this action are parametrized by …
Limits of Bessel functions for root systems as the rank tends to infinity Open
We study the asymptotic behaviour of Bessel functions associated to root systems of type An−1 and type Bn with positive multiplicities as the rank n tends to infinity. In both cases, we characterize the possible limit functions and the Ver…
Limits of Bessel functions for root systems as the rank tends to infinity Open
We study the asymptotic behaviour of Bessel functions associated of root systems of type $A_{n-1}$ and type $B_n$ with positive multiplicities as the rank $n$ tends to infinity. In both cases, we characterize the possible limit functions a…
The Dunkl-Laplace transform and Macdonald's hypergeometric series Open
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 transform identity for Heckman-Opdam hypergeometric function…
View article: Elementary symmetric polynomials and martingales for Heckman-Opdam processes
Elementary symmetric polynomials and martingales for Heckman-Opdam processes Open
We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$…
Beta Distributions and Sonine Integrals for Bessel Functions on Symmetric Cones Open
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 μ. For Bessel functions on matrix cones, Sonine formulas involve b…