Ramanujans master theorem for Riemannian symmetric spacesReport as inadecuate

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1 Lousiana State University 2 Analyse IECL - Institut Élie Cartan de Lorraine

Abstract : Ramanujan-s Master theorem states that, under suitable conditions, the Mellin transform of a power series provides an interpolation formula for the coefficients of this series. Based on the duality of compact and non-compact reductive Riemannian symmetric spaces inside a common complexification, we prove an analogue of Ramanujan-s Master Theorem for the spherical Fourier transform of a spherical Fourier series. This extends the results proven by Bertram for Riemannian symmetric spaces of rank-one.

Keywords : Holomorphic extension Spherical Fourier series Ramanujanʼs Master Theorem Integral interpolation formulas Symmetric spaces Spherical transform

Author: Gestur Olafsson - Angela Pasquale -

Source: https://hal.archives-ouvertes.fr/


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