# Radon transform on spheres and generalized Bessel function associated with dihedral groups

Abstract : 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 D2(2p), p ≥ 1 when both multiplicities sum to an integer. In particular, we recover a previous result obtained for D2(4) and we give a special interest to D2(6). The paper is closed with adapting our method to odd dihedral groups thereby exhausting the list of Weyl dihedral groups.
Type de document :
Pré-publication, Document de travail
2010
Domaine :

https://hal.archives-ouvertes.fr/hal-00519722
Contributeur : Nizar Demni <>
Soumis le : mardi 21 septembre 2010 - 11:54:49
Dernière modification le : jeudi 27 avril 2017 - 09:46:24
Document(s) archivé(s) le : mardi 23 octobre 2012 - 16:25:35

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Gegen-Fourier.pdf
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### Identifiants

• HAL Id : hal-00519722, version 1

### Citation

Nizar Demni. Radon transform on spheres and generalized Bessel function associated with dihedral groups. 2010. <hal-00519722>

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