An analogue of Hardy’s theorem for very rapidly decreasing functions on semi-simple Lie groups

A. Sitaram and M. Sundari

Vol. 177 (1997), No. 1, 187–200

DOI: 10.2140/pjm.1997.177.187

Abstract

We generalise a result of Hardy, which asserts the impossibility of a function and its Fourier transform to be simultaneously “very rapidly decreasing”, to: (i) all noncompact, semi-simple Lie groups with one conjugacy class of Cartan subgroups; (ii) SL(2, ℝ); and (iii) all symmetric spaces of the noncompact type.

Milestones

Received: 3 May 1995

Revised: 29 November 1995

Published: 1 January 1997