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arXiv · 2606.04524

Uniqueness results for quasi-analytic functions on compact Lie groups and homogeneous spaces

Mithun Bhowmik·Sanjib Pradhan
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Abstract

In this article, we establish a quantitative uniqueness theorem for quasi-analytic functions defined on compact, connected Lie groups $G$ and on homogeneous spaces $G/H$, where $H$ is any closed subgroup of $G$. Our result extends classical Logvinenko-Sereda-type theorems to the setting of quasi-analytic functions on compact Lie groups and their homogeneous spaces. We introduce the quasi-analytic class of functions using iterates of the Casimir operator on $G$. This construction is justified by establishing that every function in this class possesses the strong unique continuation property. In particular, our result extends a result of P. Chernoff (Bull. Amer. Math. Soc., 1975) to the framework of compact Lie groups and their homogeneous spaces.

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Mithun Bhowmik, Sanjib Pradhan. 2026-06-03. Uniqueness results for quasi-analytic functions on compact Lie groups and homogeneous spaces. https://arxiv.org/abs/2606.04524

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