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arXiv · 1901.03196

Analogs of certain quasi-analiticity results on Riemannian symmetric spaces of noncompact type

Mithun Bhowmik·Sanjoy Pusti·Swagato K. Ray
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Abstract

An $L^2$ version of the celebrated Denjoy-Carleman theorem regarding quasi-analytic functions was proved by Chernoff \cite{CR} on $\mathbb R^d$ using iterates of the Laplacian. In $1934$ Ingham \cite{I} used the classical Denjoy-Carleman theorem to relate the decay of Fourier transform and quasi-analyticity of integrable functions on $\mathbb R$. In this paper we extend both these theorems to Riemannian symmetric spaces of noncompact type and show that the theorem of Ingham follows from that of Chernoff.

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Mithun Bhowmik, Sanjoy Pusti, Swagato K. Ray. 2019-01-09. Analogs of certain quasi-analiticity results on Riemannian symmetric spaces of noncompact type. https://arxiv.org/abs/1901.03196

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