Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$
Ben Salem, Néjib ; El Garna, Anis ; Kallel , Samir
Methods Appl. Anal., Tome 15 (2008) no. 1, p. 477-494 / Harvested from Project Euclid
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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.
Publié le : 2008-12-15
Classification:  Dunkl operator,  Poisson transform,  heat transform,  Bessel potential,  Flett potential,  32A55,  47H5O,  31A1O 
@article{1254492830,
     author = {Ben Salem, N\'ejib and El Garna, Anis and Kallel , Samir},
     title = {Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$},
     journal = {Methods Appl. Anal.},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 477-494},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1254492830}
}

Ben Salem, Néjib; El Garna, Anis; Kallel , Samir. Bessel and Flett Potentials associated with Dunkl Operators on $\Bbb R^d$. Methods Appl. Anal., Tome 15 (2008) no. 1, pp.  477-494. http://gdmltest.u-ga.fr/item/1254492830/