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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
