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Strichartz estimates for the Schrödinger equation on non-rectangular two-dimensional tori
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 144, Number 3, June 2022
- pp. 701-745
- 10.1353/ajm.2022.0014
- Article
- Additional Information
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Abstract
abstract:
We propose a conjecture for long time Strichartz estimates on generic (non-rectangular) flat tori. We proceed to partially prove it in dimension 2. Our arguments involve on the one hand Weyl bounds; and on the other hands bounds on the number of solutions of Diophantine problems.
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