Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application to a conjecture of Strichartz

摘要

In this paper we develop the scattering theory for the Laplacian on symmetric spaces of noncompact type. We study the asymptotic properties of the resolvent in the framework of the Agmon-Hormander space. Our approach is based on a detailed analysis of the Helgason Fourier transform and generalized spherical functions on symmetric spaces of noncompact type. As an application of our scattering theory, we prove a conjecture by Strichartz concerning a characterization of a family of generalized eigenfunctions of the Laplacian. (C) 2018 Elsevier Inc. All rights reserved.