Reference : Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/26293
Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications
English
Narayanan, E.K. []
Pasquale, Angela []
Pusti, Sanjoy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2014
Advances in Mathematics
Academic Press
252
227–259
Yes (verified by ORBilu)
0001-8708
1090-2082
San Diego
CA
[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 $1\leq p <2$.
http://hdl.handle.net/10993/26293
10.1016/j.aim.2013.10.027

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