Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

Narayanan, EK and Pasquale, A and Pusti, S (2014) Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications. In: ADVANCES IN MATHEMATICS, 252 . pp. 227-259.

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Abstract

A series expansion for Heckman-Opdam hypergeometric functions phi(lambda) is obtained for all lambda is an element of alpha(C)*. As a consequence, estimates for phi(lambda) away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The L-P-theory for the hypergeometric Fourier transform is developed for 0 < p < 2. In particular, an inversion formula is proved when 1 <= p < 2. (C) 2013 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	ADVANCES IN MATHEMATICS
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Additional Information:	Copyright for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, USA
Keywords:	Hypergeometric functions; Harish-Chandra series expansion; Spherical functions; Root systems; Cherednik operators; Hypergeometric Fourier transform
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	06 Mar 2014 06:50
Last Modified:	06 Mar 2014 06:50
URI:	http://eprints.iisc.ac.in/id/eprint/48491

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