Analogs of certain quasi-analiticity results on Riemannian symmetric spaces of noncompact type

Abstract

An L 2 version of the celebrated Denjoy-Carleman theorem regarding quasianalytic functions was proved by Chernoff [10] on R d using iterates of the Laplacian. In 1934 Ingham [23] used the classical Denjoy-Carleman theorem to relate the decay of Fourier transform and quasi-analyticity of integrable functions on R. In this paper we extend both these theorems to Riemannian symmetric spaces of noncompact type and show that the theorem of Ingham follows from that of Chernoff.