非矩形二维环面Schrödinger方程的Strichartz估计

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2022-06-01 DOI:10.1353/ajm.2022.0014

Yu Deng, P. Germain, L. Guth, Simon Leo Rydin Myerson

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引用次数: 3

摘要

提出了一般(非矩形)平面环面上的长时间Strichartz估计的一个猜想。我们继续在二维中部分证明它。我们的论证一方面涉及Weyl界;另一方面是丢番图问题的解的数目的界限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Strichartz estimates for the Schrödinger equation on non-rectangular two-dimensional tori

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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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.