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arXiv · 2509.23965

Observability of Schr\"odinger propagators on tori in rough settings

Nicolas Burq·Hui Zhu
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Abstract

On tori of arbitrary dimensions, Schr\"odinger propagators with bounded potentials are conjectured to be observable from space-time domains of positive Lebesgue measure. We reduce this conjecture to certain integrability bounds for free Schr\"odinger waves, thereby proving the conjecture on the one-dimensional torus and producing new examples of observation domains. These bounds are far weaker than Bourgain's conjectured periodic Strichartz estimates, yet remain highly nontrivial.

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Nicolas Burq, Hui Zhu. 2025-09-28. Observability of Schr\"odinger propagators on tori in rough settings. https://arxiv.org/abs/2509.23965

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