Asymptotic Analysis for the Dunkl Kernel

Authors: Rösler M.¹; de Jeu M.²

Source: Journal of Approximation Theory, Volume 119, Number 1, November 2002 , pp. 110-126(17)

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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 ₁F₁ 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. © 2002 Elsevier Science (USA).

Keywords: Dunkl operators; Dunkl kernel; asymptotics.

Language: English

Document Type: Research article

DOI: http://dx.doi.org/10.1006/jath.2002.3722

Affiliations: 1: Universität Göttingen, Bunsenstr. 3-5, Göttingen, D-37073, Germany 2: University of Amsterdam, Plantage Muidergracht 24, Amsterdam, TV, 1018, The Netherlands

Publication date: 2002-11-01