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Pré-Publication, Document De Travail Année : 2010

Radon Transform on spheres and generalized Bessel function associated with dihedral groups

Nizar Demni
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Résumé

Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas for Fourier and Radon transforms to derive a closed formula for this series when the parameter of the Gegenbauer polynomial is a strictly positive integer. As a by-product, we get a relatively simple integral representation for the generalized Bessel function associated with even dihedral groups when both multiplicities sum to an integer. In particular, we recover a previous result obtained for the square symmetries-preserving group and we give a special interest to the hexagon. The paper is closed with adapting our method to odd dihedral groups thereby exhausting the list of Weyl dihedral groups.

Dates et versions

hal-00554299 , version 1 (10-01-2011)

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Citer

Nizar Demni. Radon Transform on spheres and generalized Bessel function associated with dihedral groups. 2010. ⟨hal-00554299⟩
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