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December 2008 Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$
Néjib Ben Salem, Anis El Garna, Samir Kallel
Methods Appl. Anal. 15(4): 477-494 (December 2008).


Analogous of Bessel and Flett potentials are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflection group. We show that the Dunkl-Bessel potentials, of positive order, can be represented by an integral involving the k-heat transform and we give some applications of this result. Also, we obtain an explicit inversion formula for the Dunkl-Flett potentials, which are interpreted as negative fractional powers of a certain operator expressed in terms of the Dunkl-Laplacian.


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Néjib Ben Salem. Anis El Garna. Samir Kallel . "Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$." Methods Appl. Anal. 15 (4) 477 - 494, December 2008.


Published: December 2008
First available in Project Euclid: 2 October 2009

zbMATH: 1221.31009
MathSciNet: MR2550074

Primary: 31A1O , 32A55 , 47H5O

Keywords: Bessel potential , Dunkl operator , Flett potential , heat transform , Poisson transform

Rights: Copyright © 2008 International Press of Boston


Vol.15 • No. 4 • December 2008
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