标题： 在粗糙设置下环面上的薛定谔传播算子的可观测性 显示英文标题

标题： Observability of Schrödinger propagators on tori in rough settings

摘要： 在一个任意维数的环面上，猜想带有有界势的薛定谔传播器可以从任何具有正勒贝格测度的空间-时间集合中被观测到。我们建立了一个准则，该准则在一条维数环面上证明了该猜想，给出了新的可测观测集合的例子，并且更为重要的是，将一般的猜想简化为验证自由薛定谔波的某些可积性界限。这些界限远弱于布尔加因猜想的周期性斯特里哈茨估计，但仍具有高度非平凡性。 显示英文摘要

摘要： On a torus of arbitrary dimension, it is conjectured that Schr\"odinger propagators with bounded potentials are observable from any space-time set of positive Lebesgue measure. We establish a criterion that proves the conjecture on the one-dimensional torus, yields new examples of measurable observation sets, and, more significantly, reduces the general conjecture to verifying certain integrability bounds for free Schr\"odinger waves. These bounds are far weaker than Bourgain's conjectured periodic Strichartz estimates, yet remain highly nontrivial.