Vol. 177, No. 1, 1997

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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
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, ); and (iii) all symmetric spaces of the noncompact type.

Milestones
Received: 3 May 1995
Revised: 29 November 1995
Published: 1 January 1997
Authors
A. Sitaram
Indian Statistical Institute
8th Mile, Mysore Road
Bangalore - 560 059
India
M. Sundari
Indian Statistical Institute
8th Mile, Mysore Road
Bangalore - 560 059
India