Asymptotic analysis for the Dunkl kernel

Abstract

This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain. The obtained results are based on the asymptotic analysis of an associated system of ordinary differential equations. They generalize the well-known asymptotics of the confluent hypergeometric function ${}_1{F}_1$ to the higher-dimensional setting and include a complete short-time asymptotics for the Dunkl-type heat kernel. As an application, it is shown that the representing measures of Dunkl's intertwining operator are generically continuous.

LaTeX2e, 16 pages, 1 figure. Second and final version, with minor corrections. Mathematically identical to first version. Accepted by Journal of Approximation Theory

Cited by in corpus (3)

• Paley-Wiener theorems for the Dunkl transform
• On the Path Integral Formulation of Wigner-Dunkl Quantum Mechanics
• Absolute continuity of the measures of the Dunkl intetwining operator and its dualand applications