A Theorem of Chernoff on Quasi-analytic Functions for Riemannian Symmetric Spaces

An L-2 version of the classical Denjoy-Carleman theorem regarding quasi-analytic functions was proved by P. Chernoff on R-n using iterates of the Laplacian. We give a simple proof of this theorem that generalizes the result on R-n for any p is an element of [1, 2]. We then extend this result to Riemannian symmetric spaces of compact and noncompact type for K-biinvariant functions.

Automated summary

This article presents a method used by P. Chernoff to prove the L-2 version of the classical Denjoy-Carleman theorem using iterates of the Laplacian on R-n, and extends it to the general case and Riemannian symmetric spaces.