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 Charles F. Dunkl in papers published in 1989 and 1988 respectively, The Dunkl operators and their various modifications have stimulated considerable developments in a number of fields. There have been applications in classical analysis, mathematical physics, special functions, Lie theory, quantum groups, algebra, probability theory, and geometry.

This issue is devoted to the 20th anniversary of Dunkl operators.

Possible topics for papers include

• orthogonal polynomials and approximation theory in several variables;
• special functions associated with root systems;
• integral transforms and Fourier analysis;
• exactly solvable quantum-mechanical models of Calogero-Moser-Sutherland type;
• Hecke and Cherednik algebras and their representations;
• quantum groups;
• complex reflection groups and Clifford algebra;
• random processes.

How to Submit an Article to the Issue.

The length of an article is not limited.

Publication will be done only on the results of the peer review according to refereeing policy of SIGMA.

Papers in this Issue:

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 ]

Forthcoming papers: