Fourier series on compact symmetric spaces: K-finite functions of small support

TY - JOUR

T1 - Fourier series on compact symmetric spaces: K-finite functions of small support

AU - Schlichtkrull, Henrik

AU - olafsson, gestur

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

M3 - Journal article

SN - 1069-5869

VL - 16

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 4

ER -