A Paley–Wiener theorem for the spectral projection of symmetric graphs

Shin Koizumi

Vol. 290 (2017), No. 1, 117–137

DOI: 10.2140/pjm.2017.290.117

Abstract

We prove a Paley–Wiener theorem for the spectral projection of symmetric graphs and, as a corollary, derive a Paley–Wiener theorem for the Helgason–Fourier transform. The proof is based on contour integration arguments similar to those used to prove the Paley–Wiener theorem for Euclidean spaces and symmetric spaces.

Keywords

spectral projection, symmetric graph, Paley–Wiener theorem, generalized spherical function

Mathematical Subject Classification 2010

Primary: 43A80

Secondary: 43A85

Milestones

Received: 28 August 2016

Revised: 29 January 2017

Accepted: 7 March 2017

Published: 7 July 2017