Resolvent bounds imply observability from measurable time sets for Schr\"odinger equations

Nicolas Burq; Hui Zhu

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arXiv · 2510.24517

Resolvent bounds imply observability from measurable time sets for Schr\"odinger equations

Nicolas Burq·Hui Zhu

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Abstract

We prove that on a compact Riemannian manifold, resolvent bounds for the Laplace--Beltrami operator imply observability, and thus controllability, for the Schr\"odinger propagator from time sets of positive Lebesgue measure. Applications include almost all cases where observability and controllability hold from time intervals, particularly when the geometric control condition is satisfied or when the manifold is a compact surface of negative curvature.

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Nicolas Burq, Hui Zhu. 2025-10-28. Resolvent bounds imply observability from measurable time sets for Schr\"odinger equations. https://arxiv.org/abs/2510.24517

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