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Journal of Lie Theory 29 (2019), No. 1, 095--106
Copyright Heldermann Verlag 2019

An Integral Transform Connecting Spherical Analysis on Harmonic NA Groups to that of Odd Dimensional Real Hyperbolic Spaces

Ahmed Intissar
University of Rabat, Morocco

M. V. Ould Moustapha
Department of Mathematics, College of Science and Arts, University of Aljouf, El-Qurayat, Saudi Arabia

Zakariyae Mouhcine
CeReMAR - L.A.M.A., Department of Mathematics, Faculty of Sciences, Mohammed V University, Rabat, Morocco

The main aim of the present paper is to establish an integral transform connecting spherical analysis on harmonic NA groups to that of odd dimensional real hyperbolic spaces. Moreover, certain interesting integral identities for the Gauss hypergeometric functions have also been given.

Keywords: Harmonic NA groups, hyperbolic spaces, Laplace-Beltrami operator, resolvent kernel, Gauss hypergeometric function, Jacobi equation, hyperbolic functions.

MSC: 44A20, 33C05, 53C35

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