A Theorem of Chernoff on Quasi-analytic Functions for Riemannian Symmetric Spaces
International Mathematics Research Notices
An L2 version of the classical Denjoy–Carleman theorem regarding quasi-analytic functions was proved by P. Chernoff on Rn using iterates of the Laplacian. We give a simple proof of this theorem that generalizes the result on Rn for any p∈[1,2]. We then extend this result to Riemannian symmetric spaces of compact and noncompact type for K-biinvariant functions.
Bhowmik, Mithun; Pusti, Sanjoy; and Ray, Swagato K., "A Theorem of Chernoff on Quasi-analytic Functions for Riemannian Symmetric Spaces" (2021). ISI Best Publications. 25.