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 quasi-analytic functions was proved by Chernoff \cite{CR} on ${\mathbb{R}}^d$ using iterates of the Laplacian. In $1934$ Ingham \cite{I} used the classical Denjoy-Carleman theorem to relate the decay of Fourier transform and quasi-analyticity of integrable functions on $\mathbb{R}$. 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.

arXiv admin note: text overlap with arXiv:1808.09710