Quantitative uniqueness and observability theorems for quasi-analytic functions on compact manifolds, generalizing Logvinenko-Sereda results and Kukavica-Li to infinite sums with energy decay.
Spectral Inequalities for the Schr{\"o}dinger operator
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abstract
In this paper we deal with the so-called "spectral inequalities", which yield a sharp quantification of the unique continuation for the spectral family associated with the Schr\"odinger operator in $ \mathbb{R}^d$ \begin{equation*} H_{g,V} = \Delta_g + V(x), \end{equation*} where $\Delta_g$ is the Laplace-Beltrami operator with respect to an analytic metric $g$, which is a perturbation of the Euclidean metric, and $V(x)$ a real valued analytic potential vanishing at infinity.
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2026 1verdicts
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Quantitative uniqueness properties for functions on compact quasi-analytic manifolds
Quantitative uniqueness and observability theorems for quasi-analytic functions on compact manifolds, generalizing Logvinenko-Sereda results and Kukavica-Li to infinite sums with energy decay.