Vol. 192, No. 2, 2000

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Hardy’s Uncertainty Principle on semisimple groups

M. Cowling, A. Sitaram and M. Sundari

Vol. 192 (2000), No. 2, 293–296
Abstract

A theorem of Hardy states that, if f is a function on such that |f(x)|≤ C eα|x|2 for all x in and |f(ξ)|≤ C eβ|ξ|2 for all ξ in , where α > 0, β > 0, and αβ > 14, then f = 0. Sitaram and Sundari generalised this theorem to semisimple groups with one conjugacy class of Cartan subgroups and to the K-invariant case for general semisimple groups. We extend the theorem to all semisimple groups.

Milestones
Received: 26 June 1998
Published: 1 February 2000
Authors
M. Cowling
University of New South Wales
Sydney NSW 2052
Australia
A. Sitaram
Indian Statistical Institute
Bangalore - 560 059
India
M. Sundari
University of New South Wales
Sydney NSW 2052
Australia
P.O. Box No. 5978
Jeddah 21432
Kingdom of Saudi Arabia