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Asymptotic analysis for the Dunkl kernel

Margit Rösler·Marcel de Jeu
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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 $\phantom{}_1F_1$ 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.

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Margit Rösler, Marcel de Jeu. 2002-02-09. Asymptotic analysis for the Dunkl kernel. https://doi.org/10.1006/jath.2002.3722

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