The uncertainty principle on Riemannian symmetric spaces of the noncompact type

Abstract

The uncertainty principle in R n {\mathcal R}^{n} says that it is impossible for a function and its Fourier transform to be simultaneously very rapidly decreasing. A quantitative assertion of this principle is Hardy’s theorem. In this article we prove various generalisations of Hardy’s theorem for Riemannian symmetric spaces of the noncompact type. In the case of the real line these results were obtained by Morgan and Cowling-Price.