The Fourier coefficients of a smooth K-invariant function on a compact symmetric space M = U / K are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we describe the size of the support by means of the exponential type of a holomorphic extension of the Fourier coefficients. © 2007 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Advances in Mathematics
Ólafsson, G., & Schlichtkrull, H. (2008). A local Paley-Wiener theorem for compact symmetric spaces. Advances in Mathematics, 218 (1), 202-215. https://doi.org/10.1016/j.aim.2007.11.021