arXiv subjects

Sanjib Pradhan

Publications and source records attributed to Sanjib Pradhan.

2 recordsLinked to original sources

arXiv2026

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

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.

math.FA↗

arXiv2026

Quantitative uniqueness properties for functions on compact quasi-analytic manifolds

In this article, we establish quantitative uniqueness results for a class of functions defined on a quasi-analytic compact manifold $X$ without boundary. This function class is characterized by the iterates of a positive elliptic linear differential operator on $X$ and, notably, encompasses all functions with a finite spectrum. By employing a relatively dense observable set, we extend classical Logvinenko-Sereda-type results to this quasi-analytic framework. Furthermore, we demonstrate that if these functions satisfy a doubling property, observability holds from any measurable set of positive measure. Our results generalise the propagation of smallness from finite sums of eigenfunctions to infinite sums with an appropriate energy-parameter decay, thereby extending recent findings by Kukavica-Li (Proc. Lond. Math. Soc., 2025) to the quasi-analytic setting.

math.FA↗