Vol. 249, No. 1, 2011

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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
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
Authors
E. K. Narayanan
Indian Institute of Science
Department of Mathematics
Bangalore 560012
India
http://www.math.iisc.ernet.in/~naru
Alladi Sitaram
Indian Institute of Science
Department of Mathematics
Bangalore 560012
India