A theorem of Chernoff on quasi-analytic functions for Riemannian symmetric spaces

2021/03/13 by Bhowmik, Mithun, Pusti, Sanjoy, Ray, Swagato K · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.07667

Abstract

An L² version of the classical Denjoy-Carleman theorem regarding quasi-analytic functions was proved by P. Chernoff on \mathbb Rⁿ using iterates of the Laplacian. We give a simple proof of this theorem which generalizes the result on \mathbb Rⁿ for any p∈ [1, 2]. We then extend this result to Riemannian symmetric spaces of compact and noncompact type for K-biinvariant functions.

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