Hardy’s Uncertainty Principle on semisimple groups

M. Cowling, A. Sitaram and M. Sundari

Vol. 192 (2000), No. 2, 293–296

DOI: 10.2140/pjm.2000.192.293

Abstract

A theorem of Hardy states that, if f is a function on ℝ such that |f(x)|≤ C e^−α|x|2 for all x in ℝ and |f(ξ)|≤ C e^−β|ξ|2 for all ξ in ℝ, where α > 0, β > 0, and αβ > 1∕4, 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