Quasi-analytic $L^p$-functions on Riemannian symmetric spaces of noncompact type, a theorem of Chernoff

Rudra P. Sarkar

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arXiv · 2112.00477

Quasi-analytic $L^p$-functions on Riemannian symmetric spaces of noncompact type, a theorem of Chernoff

Rudra P. Sarkar

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Abstract

A result of Chernoff gives sufficient condition for an $L^2$-function on $\R^n$ to be quasi-analytic. This is a generalization of the classical Denjoy-Carleman theorem on $\R$ and of the subsequent work on $\R^n$ by Bochner and Taylor. In this note we endeavour to obtain an exact analogue of the result of Chernoff for $L^p, p\in [1,2]$ functions on the Riemannian symmetric spaces of noncompact type. No restriction on the rank of the symmetric spaces and no condition on the symmetry of the functions is assumed.

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BibTeX RIS

Rudra P. Sarkar. 2021-12-01. Quasi-analytic $L^p$-functions on Riemannian symmetric spaces of noncompact type, a theorem of Chernoff. https://arxiv.org/abs/2112.00477

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