Observability of Schr\"odinger propagators on tori in rough settings
Analysis of PDEs
2025-10-23 v2 Mathematical Physics
Functional Analysis
math.MP
Optimization and Control
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.
Keywords
Cite
@article{arxiv.2509.23965,
title = {Observability of Schr\"odinger propagators on tori in rough settings},
author = {Nicolas Burq and Hui Zhu},
journal= {arXiv preprint arXiv:2509.23965},
year = {2025}
}
Comments
28 pages