Reference : Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated...
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/26293
 Title : Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications Language : English Author, co-author : Narayanan, E.K. [] Pasquale, Angela [] Pusti, Sanjoy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : 2014 Journal title : Advances in Mathematics Publisher : Academic Press Volume : 252 Pages : 227–259 Peer reviewed : Yes (verified by ORBilu) ISSN : 0001-8708 e-ISSN : 1090-2082 City : San Diego Country : CA Abstract : [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

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