
Journal of Lie Theory 29 (2019), No. 1, 095106 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, ElQurayat, Saudi Arabia mohamedvall.ouldmoustapha230@gmail.com Zakariyae Mouhcine CeReMAR  L.A.M.A., Department of Mathematics, Faculty of Sciences, Mohammed V University, Rabat, Morocco zakariyaemouhcine@gmail.com 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, LaplaceBeltrami operator, resolvent kernel, Gauss hypergeometric function, Jacobi equation, hyperbolic functions. MSC: 44A20, 33C05, 53C35 [ Fulltextpdf (121 KB)] for subscribers only. 