[en] A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\l$ is obtained for all $\l \in \fa^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\l$ 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 $1\leq p <2$.
Disciplines :
Mathematics
Author, co-author :
Narayanan, E.K.
Pasquale, Angela
Pusti, Sanjoy ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications
Publication date :
2014
Journal title :
Advances in Mathematics
ISSN :
1090-2082
Publisher :
Academic Press, San Diego, United States - California