%0 Journal Article
%T Fourier series on compact symmetric spaces
%A Gestur Olafsson
%A Henrik Schlichtkrull
%J Mathematics
%D 2008
%I arXiv
%X The Fourier coefficients F(t) of a function f on a compact symmetric space U/K are given by integration of f against matrix coefficients of irreducible representations of U. The coefficients depend on a spectral parameter t, which determines the representation, and they can be represented by elements F(t) in a common Hilbert space H. We obtain a theorem of Paley-Wiener type which describes the size of the support of f by means of the exponential type of a holomorphic H-valued extension of F, provided f is K-finite and of sufficiently small support. The result was obtained previously for K-invariant functions, to which case we reduce.
%U http://arxiv.org/abs/0804.3759v3