Laplace-type integral representations of the generalized Bessel function\n and of the Dunkl kernel of type B₂

2016/11/17 by Béchir Amri, Amri, Bechir, Nizar Demni +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1611.05696

openalex publication_date 2016/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive a Laplace-type integral representations for both the\ngeneralized Bessel function and the Dunkl kernel associated with the rank-two\nroot system of type B₂. The derivation of the first one elaborates on the\nintegral representation of the generalized Bessel function proved in\n citeDemni through the modified Bessel function of the first kind. In\nparticular, we recover an expression of the density of the Duistermaat-Heckman\nmeasure for the dihedral group of order eight. As to the integral\nrepresentation of the corresponding Dunkl kernel, it follows from an\napplication of the shift principle to the generalized Bessel function.\n

Related

• Explicit formulas for the Dunkl dihedral kernel and the (κ, a)-generalized Fourier kernel
• Generalized Bessel functions of dihedral-type: expression as a series of confluent Horn functions and Laplace-type integral representation
• Dunkl kernel associated with dihedral group
• On the integral representations for Dunkl kernels of type A₂
• Uniform bounds on the Dunkl kernel