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Article Dans Une Revue Advances in Mathematics Année : 2014

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

E.K. Narayanan
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A. Pasquale

Résumé

A series expansion for Heckman-Opdam hypergeometric functions ϕ_λ is obtained for all λ ∈ a*_C . As a consequence, estimates for ϕ_λ 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.
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Dates et versions

hal-01096768 , version 1 (18-12-2014)

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E.K. Narayanan, A. Pasquale, S. Pusti. Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications. Advances in Mathematics, 2014, 252, pp.227-259. ⟨10.1016/j.aim.2013.10.027⟩. ⟨hal-01096768⟩
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