Cowling-Price theorem and characterization of heat kernel on symmetric spaces (Q1882353)

The classical Hardy's theorem states that if \(| f(x)| <Ce^{-ax^{2}}\) and \(| \hat{f}(x)| <Ce^{-bx^{2}}\) then either is \(f=0\) almost everywhere, if \(ab<1/4\), or \(f\) is a constant times the Gauss kernel, if \(ab=1/4\). In this article the authors consider variants of the second assertion on non-compact Riemannian symmetric spaces.