Ramanujan's master theorem for Riemannian symmetric spaces

Gestur Olafsson (1) , Angela Pasquale (2)

1 Lousiana State University
2 LMAM - Laboratoire de Mathématiques et Applications de Metz

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.

Mots clés: Symmetric spaces; Spherical transform; Ramanujanʼs Master Theorem; Integral interpolation formulas; Spherical Fourier series; Holomorphic extension

Domaines: Mathématiques [math]

Gestur Olafsson, Angela Pasquale. Ramanujan's master theorem for Riemannian symmetric spaces. Journal of Functional Analysis, 2012, 262 (11), pp.4851-4890. ⟨10.1016/j.jfa.2012.03.006⟩. ⟨hal-01234565⟩