The Fourier coefficients 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 μ, which determines the representation, and they can be represented by elements f̂(μ) 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 f̂, provided f is K-finite and of sufficiently small support. The result was obtained previously for K-invariant functions, to which case we reduce. © 2010 Springer Science+Business Media, LLC.
Publication Source (Journal or Book title)
Journal of Fourier Analysis and Applications
Ólafsson, G., & Schlichtkrull, H. (2010). Fourier series on compact symmetric spaces: K-finite functions of small support. Journal of Fourier Analysis and Applications, 16 (4), 609-628. https://doi.org/10.1007/s00041-010-9122-9