
The Guest Editors for this special issue are
Charles Dunkl (University of Virginia, USA)
Peter Forrester (University of Melbourne, Australia)
Marcel de Jeu (Leiden University, the Netherlands)
Margit Rösler (Technische Universität Clausthal, Germany)
Yuan Xu (University of Oregon, USA)
The original Dunkl operators and the associated Laplacian were defined by
the undersigned in papers published in 1989 and 1988 respectively. The
guiding idea was to use finite reflection groups to provide structure for
multivariable analysis. Twenty years later this special issue demonstrates
that these methods are useful in harmonic analysis, integral transforms,
probabilistic processes, special functions, quantummechanical integrable
systems, differential equations, algebras associated to Coxeter groups, some
aspects of representation theory and other topics. We thank the authors and
the referees for their work and interest in the special issue. I gratefully
acknowledge the efforts and valuable contributions of my fellow editors.
Charles F. Dunkl
Papers in this Issue:

Dunkl Operators and Canonical Invariants of Reflection Groups

Arkady Berenstein and Yurii Burman
SIGMA 5 (2009), 057, 18 pages [ abs
pdf ps ]

Hilbert Transforms Associated with DunklHermite Polynomials

Néjib Ben Salem and Taha Samaali
SIGMA 5 (2009), 037, 17 pages [ abs
pdf ps ]

Nonlocal Operational Calculi for Dunkl Operators

Ivan H. Dimovski and Valentin Z. Hristov
SIGMA 5 (2009), 030, 16 pages [ abs
pdf ps ]

Inversion Formulas for the Spherical RadonDunkl Transform

Zhongkai Li and Futao Song
SIGMA 5 (2009), 025, 15 pages [ abs
pdf ps ]

BesovType Spaces on R^{d} and Integrability for the Dunkl Transform

Chokri Abdelkefi, JeanPhilippe Anker, Feriel Sassi and Mohamed Sifi
SIGMA 5 (2009), 019, 15 pages [ abs
pdf ps ]

Imaginary Powers of the Dunkl Harmonic Oscillator

Adam Nowak and Krzysztof Stempak
SIGMA 5 (2009), 016, 12 pages [ abs
pdf ps ]

HeckeClifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type

Ta Khongsap and Weiqiang Wang
SIGMA 5 (2009), 012, 27 pages [ abs
pdf ps ]

The Rational qKZ Equation and Shifted NonSymmetric Jack Polynomials

Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito and Yoshihiro Takeyama
SIGMA 5 (2009), 010, 12 pages [ abs
pdf ps ]

An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian

Hendrik De Bie
SIGMA 4 (2008), 093, 11 pages [ abs
pdf ps ]

Sonine Transform Associated to the Dunkl Kernel on the Real Line

Fethi Soltani
SIGMA 4 (2008), 092, 14 pages [ abs
pdf ps ]

External Ellipsoidal Harmonics for the DunklLaplacian

Hans Volkmer
SIGMA 4 (2008), 091, 13 pages [ abs
pdf ps ]

Symmetries of Spin Calogero Models

Vincent Caudrelier and Nicolas Crampé
SIGMA 4 (2008), 090, 15 pages [ abs
pdf ps ]

A Probablistic Origin for a New Class of Bivariate Polynomials

Michael R. Hoare and Mizan Rahman
SIGMA 4 (2008), 089, 18 pages [ abs
pdf ps ]

Dunkl Hyperbolic Equations

Hatem Mejjaoli
SIGMA 4 (2008), 084, 22 pages [ abs
pdf ps ]

A Limit Relation for DunklBessel Functions of Type A and B

Margit Rösler and Michael Voit
SIGMA 4 (2008), 083, 9 pages [ abs
pdf ps ]

Some Orthogonal Polynomials in Four Variables

Charles F. Dunkl
SIGMA 4 (2008), 082, 9 pages [ abs
pdf ps ]

Liouville Theorem for Dunkl Polyharmonic Functions

Guangbin Ren and Liang Liu
SIGMA 4 (2008), 076, 6 pages [ abs
pdf ps ]

Generalized Bessel function of Type D

Nizar Demni
SIGMA 4 (2008), 075, 7 pages [ abs
pdf ps ]

First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes

Nizar Demni
SIGMA 4 (2008), 074, 14 pages [ abs
pdf ps ]

Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions

Khalifa Trimèche
SIGMA 4 (2008), 067, 22 pages [ abs
pdf ps ]
 