Laplace-type integral representations of the generalized Bessel function and of the Dunkl kernel of type $B_2$ - Archive ouverte HAL
Article Dans Une Revue Moscow Mathematical Journal Année : 2017

Laplace-type integral representations of the generalized Bessel function and of the Dunkl kernel of type $B_2$

Résumé

In this paper, we derive a Laplace-type integral representations for both the generalized Bessel function and the Dunkl kernel associated with the rank-two root system of type B_2. The derivation of the first one elaborates on the integral representation of the generalized Bessel function proved in \cite{Demni} through the modified Bessel function of the first kind. In particular, we recover an expression of the density of the Duistermaat-Heckman measure for the dihedral group of order eight. As to the integral representation of the corresponding Dunkl kernel, it follows from an application of the shift principle to the generalized Bessel function.

Dates et versions

hal-01410457 , version 1 (06-12-2016)

Identifiants

Citer

Bechir Amri, Nizar Demni. Laplace-type integral representations of the generalized Bessel function and of the Dunkl kernel of type $B_2$. Moscow Mathematical Journal, 2017, 17 (2), pp.175-190. ⟨10.17323/1609-4514-2017-17-2-175-190⟩. ⟨hal-01410457⟩
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