Analogues of the Wiener Tauberian and Schwartz theorems for radial functions on symmetric spaces

E. K. Narayanan and Alladi Sitaram

Vol. 249 (2011), No. 1, 199–210

DOI: 10.2140/pjm.2011.249.199

Abstract

We prove a Wiener Tauberian theorem for the L¹ spherical functions on a semisimple Lie group of arbitrary real rank. We also establish a Schwartz-type theorem for complex groups. As a corollary we obtain a Wiener Tauberian type result for compactly supported distributions.

Keywords

Wiener Tauberian theorems, Schwartz theorems, maximal ideals, Schwartz space

Mathematical Subject Classification 2000

Primary: 43A20, 43A90

Secondary: 43A80, 43A30

Milestones

Received: 10 November 2009

Accepted: 16 February 2010

Published: 3 January 2011