Observability of Schrödinger propagators on tori in rough settings
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917033588817920 |
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| author | Burq, Nicolas Zhu, Hui |
| author_facet | Burq, Nicolas Zhu, Hui |
| contents | On tori of arbitrary dimensions, Schrödinger 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Observability of Schrödinger propagators on tori in rough settings Burq, Nicolas Zhu, Hui Analysis of PDEs Mathematical Physics Functional Analysis Optimization and Control On tori of arbitrary dimensions, Schrödinger 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 Schrödinger 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. |
| title | Observability of Schrödinger propagators on tori in rough settings |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2509.23965 |