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- Margit Rösler
- 1997

Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on R . The definition and properties of these generalized Hermite systems extend naturally those of their classical counterparts; partial derivatives and the usual… (More)

- Margit Rösler
- 2002

These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform. We point out the connection with integrable… (More)

- MARGIT RÖSLER
- 2002

It is an open conjecture that generalized Bessel functions associated with root systems have a positive product formula for non-negative multiplicity parameters of the associated Dunkl operators. In this paper, a partial result towards this conjecture is proven, namely a positive radial product formula for the non-symmetric counterpart of the generalized… (More)

- MARGIT RÖSLER
- 1999

For a finite reflection group on R , the associated Dunkl operators are parametrized firstorder differential-difference operators which generalize the usual partial derivatives. They generate a commutative algebra which is – under weak assumptions – intertwined with the algebra of partial differential operators by a unique linear and homogeneous isomorphism… (More)

- Margit Rösler
- 2005

In this paper we introduce probability-preserving convolution algebras on cones of positive semidefinite matrices over one of the division algebras F = R,C or H which interpolate the convolution algebras of radial bounded Borel measures on a matrix space Mp,q(F) with p > q. Radiality in this context means invariance under the action of the unitary group… (More)

- Margit Rösler
- 2009

In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the (skew) fields F =… (More)

- Margit Rösler, Marcel de Jeu
- Journal of Approximation Theory
- 2002

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 infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain. The obtained results are based on the asymptotic analysis of an… (More)

- Margit Rösler
- 2003

We present a construction of a wavelet-type orthonormal basis for the space of radial L-functions in R via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by usual dilations and generalized translations. Hereby the generalized translation reveals the group convolution of radial functions… (More)

We prove a limit relation for the Dunkl–Bessel function of type BN with multiplicity parameters k1 on the roots ±ei and k2 on ±ei ± ej where k1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkltype Bessel function of type AN−1 with multiplicity k2. For certain values of k2 an improved estimate is… (More)

Dunkl operators are differential-difference operators on R which generalize partial derivatives. They lead to generalizations of Laplace operators, Fourier transforms, heat semigroups, Hermite polynomials, and so on. In this paper we introduce two systems of biorthogonal polynomials with respect to Dunkl’s Gaussian distributions in a quite canonical way.… (More)