On a theorem of Chernoff on rank one Riemannian symmetric spaces

Pritam Ganguly; Ramesh Manna; Sundaram Thangavelu

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arXiv · 2103.13888

On a theorem of Chernoff on rank one Riemannian symmetric spaces

Pritam Ganguly·Ramesh Manna·Sundaram Thangavelu

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Abstract

In 1975, P.R. Chernoff used iterates of the Laplacian on $\mathbb{R}^n$ to prove an $L^2$ version of the Denjoy-Carleman theorem which provides a sufficient condition for a smooth function on $\mathbb{R}^n$ to be quasi-analytic. In this paper, we prove an exact analogue of Chernoff's theorem for all rank one Riemannian symmetric spaces (of noncompact and compact types) using iterates of the associated Laplace-Beltrami operators.

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BibTeX RIS

Pritam Ganguly, Ramesh Manna, Sundaram Thangavelu. 2021-03-25. On a theorem of Chernoff on rank one Riemannian symmetric spaces. https://arxiv.org/abs/2103.13888

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