Ramanujan's Master Theorem for Riemannian symmetric spaces

Details Ramanujan's Master Theorem for Riemannian symmetric spaces Ramanujan's Master Theorem for Riemannian symmetric spaces

2011-03-26

arxiv.org/abs/1103.5126v3

Mathematics

Representation Theory

As accepted by JFA

Scientific paper

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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