Ramanujan's Master Theorem for Riemannian symmetric spaces

2011/03/26 by Gestur Ólafsson, Olafsson, Gestur, Angela Pasquale +1 · 1 citation
Mathematics · #33E20 (Secondary) #43A85 (Primary) 22E45 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1103.5126

openalex publication_date 2011/03/26 · openalex created_date 2019/07/30 · openalex updated_date 2026/08/01

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 Riemannian symmetric spaces of compact and noncompact type inside a common complexification, we prove an analogue of Ramanujan's Master Theorem for the spherical Fourier transform of a spherical Fourier series. This extend the results proven by Bertram for Riemannian symmetric spaces of rank-one.

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• Proof of a Conjectured Ramanujan Type Master Theorem for Powers of the Cosecant

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