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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
multi-variable analysis. Twenty years later this special issue demonstrates
that these methods are useful in harmonic analysis, integral transforms,
probabilistic processes, special functions, quantum-mechanical 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:
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Dunkl Operators and Canonical Invariants of Reflection Groups
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Arkady Berenstein and Yurii Burman
SIGMA 5 (2009), 057, 18 pages [ abs
pdf ps ]
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Hilbert Transforms Associated with Dunkl-Hermite Polynomials
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Néjib Ben Salem and Taha Samaali
SIGMA 5 (2009), 037, 17 pages [ abs
pdf ps ]
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Nonlocal Operational Calculi for Dunkl Operators
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Ivan H. Dimovski and Valentin Z. Hristov
SIGMA 5 (2009), 030, 16 pages [ abs
pdf ps ]
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Inversion Formulas for the Spherical Radon-Dunkl Transform
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Zhongkai Li and Futao Song
SIGMA 5 (2009), 025, 15 pages [ abs
pdf ps ]
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Besov-Type Spaces on Rd and Integrability for the Dunkl Transform
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Chokri Abdelkefi, Jean-Philippe Anker, Feriel Sassi and Mohamed Sifi
SIGMA 5 (2009), 019, 15 pages [ abs
pdf ps ]
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Imaginary Powers of the Dunkl Harmonic Oscillator
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Adam Nowak and Krzysztof Stempak
SIGMA 5 (2009), 016, 12 pages [ abs
pdf ps ]
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Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
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Ta Khongsap and Weiqiang Wang
SIGMA 5 (2009), 012, 27 pages [ abs
pdf ps ]
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The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
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Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito and Yoshihiro Takeyama
SIGMA 5 (2009), 010, 12 pages [ abs
pdf ps ]
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An Alternative Definition of the Hermite Polynomials Related to the Dunkl Laplacian
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Hendrik De Bie
SIGMA 4 (2008), 093, 11 pages [ abs
pdf ps ]
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Sonine Transform Associated to the Dunkl Kernel on the Real Line
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Fethi Soltani
SIGMA 4 (2008), 092, 14 pages [ abs
pdf ps ]
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External Ellipsoidal Harmonics for the Dunkl-Laplacian
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Hans Volkmer
SIGMA 4 (2008), 091, 13 pages [ abs
pdf ps ]
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Symmetries of Spin Calogero Models
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Vincent Caudrelier and Nicolas Crampé
SIGMA 4 (2008), 090, 15 pages [ abs
pdf ps ]
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A Probablistic Origin for a New Class of Bivariate Polynomials
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Michael R. Hoare and Mizan Rahman
SIGMA 4 (2008), 089, 18 pages [ abs
pdf ps ]
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Dunkl Hyperbolic Equations
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Hatem Mejjaoli
SIGMA 4 (2008), 084, 22 pages [ abs
pdf ps ]
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A Limit Relation for Dunkl-Bessel Functions of Type A and B
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Margit Rösler and Michael Voit
SIGMA 4 (2008), 083, 9 pages [ abs
pdf ps ]
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Some Orthogonal Polynomials in Four Variables
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Charles F. Dunkl
SIGMA 4 (2008), 082, 9 pages [ abs
pdf ps ]
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Liouville Theorem for Dunkl Polyharmonic Functions
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Guangbin Ren and Liang Liu
SIGMA 4 (2008), 076, 6 pages [ abs
pdf ps ]
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Generalized Bessel function of Type D
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Nizar Demni
SIGMA 4 (2008), 075, 7 pages [ abs
pdf ps ]
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First Hitting Time of the Boundary of the Weyl Chamber by Radial Dunkl Processes
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Nizar Demni
SIGMA 4 (2008), 074, 14 pages [ abs
pdf ps ]
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Inversion Formulas for the Dunkl Intertwining Operator and Its Dual on Spaces of Functions and Distributions
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Khalifa Trimèche
SIGMA 4 (2008), 067, 22 pages [ abs
pdf ps ]
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