Real Paley-Wiener theorems for the inverse Fourier transform on a Riemannian symmetric space

Nils Byrial Andersen

Vol. 213 (2004), No. 1, 1–13

DOI: 10.2140/pjm.2004.213.1

Abstract

We prove real Paley-Wiener theorems for the inverse Fourier transform on a semisimple Riemannian symmetric space G∕K of the noncompact type. The functions on G∕K whose Fourier transform has compact support are characterised by a L² growth condition. We also obtain real Paley-Wiener theorems for the inverse spherical transform.

Milestones

Received: 14 October 2002

Revised: 11 February 2003

Published: 1 January 2004