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

Mithun Bhowmik; Sanjoy Pusti; Swagato K Ray

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

Classical Analysis and ODEs 2021-03-16 v1

Authors: Mithun Bhowmik , Sanjoy Pusti , Swagato K Ray

Abstract

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

Keywords

quasi-analytic functions denjoy-carleman theorem riemannian symmetric spaces laplacian iterates k-biinvariant functions

Cite

@article{arxiv.2103.07667,
  title  = {A theorem of Chernoff on quasi-analytic functions for Riemannian symmetric spaces},
  author = {Mithun Bhowmik and Sanjoy Pusti and Swagato K Ray},
  journal= {arXiv preprint arXiv:2103.07667},
  year   = {2021}
}

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

Abstract

Keywords

Cite

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