Curved Ingham inequalities and observability of the toroidal Schr{ö}dinger equation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917347029155840 |
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| author | Haak, Bernhard H Jaming, Philippe Wang, Ming Wang, Yunlei |
| author_facet | Haak, Bernhard H Jaming, Philippe Wang, Ming Wang, Yunlei |
| contents | We prove that solutions of the toroidal Schr{ö}dinger equation can be observed from suitably curved space-time trajectories, thus of zero Lebesgue measure. To do so, we establish new upper and lower bounds for certain trigonometric sums along curves, in the spirit of the celebrated Ingham inequality. In a second part, we establish observability properties over arbitrarily short curves of the low-and high-frequency components separately. For the low-frequency component, we establish strong restrictions on the zero sets of the trigonometric sums under consideration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_15193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Curved Ingham inequalities and observability of the toroidal Schr{ö}dinger equation Haak, Bernhard H Jaming, Philippe Wang, Ming Wang, Yunlei Analysis of PDEs Classical Analysis and ODEs We prove that solutions of the toroidal Schr{ö}dinger equation can be observed from suitably curved space-time trajectories, thus of zero Lebesgue measure. To do so, we establish new upper and lower bounds for certain trigonometric sums along curves, in the spirit of the celebrated Ingham inequality. In a second part, we establish observability properties over arbitrarily short curves of the low-and high-frequency components separately. For the low-frequency component, we establish strong restrictions on the zero sets of the trigonometric sums under consideration. |
| title | Curved Ingham inequalities and observability of the toroidal Schr{ö}dinger equation |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2603.15193 |