For the one-dimensional Schrödinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates generalize a classical result of Kenig–Ponce–Vega and allow us to obtain pointwise convergence results associated with systems of infinitely many fermions. The maximal-in-space estimates simultaneously address an endpoint problem raised by Frank–Sabin in their work on Strichartz estimates for orthonormal systems of data, and provide a path toward proving our maximal-in-time estimates.

中文翻译：

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具有正交初始数据的Schrödinger方程的最大估计

对于一维Schrödinger方程，我们为正交初始数据系统获得了清晰的最大时间估计和最大空间估计。最大时间估计值概括了Kenig-Ponce-Vega的经典结果，并允许我们获得与无限多个费米子系统相关的逐点收敛结果。空间最大估计同时解决了Frank–Sabin在他们对正交数据系统的Strichartz估计的工作中提出的端点问题，并提供了证明我们最大时间估计的途径。