We consider the pointwise convergence problem for the solution of Schrödinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson’s problem as the simplest case and was studied in general by Cho et al. We extend their result from the case of the classical Schrödinger equation to a class of equations which includes the fractional Schrödinger equations. To achieve this, we significantly simplify their proof by completely avoiding a time localization argument.

中文翻译：

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分数次Schrödinger方程沿约束方向的逐点收敛

我们考虑沿着实际直线的给定紧致子集确定的方向对Schrödinger型方程进行求解的逐点收敛问题。这个问题是最简单的情况，其中包含Carleson问题，Cho等人对此进行了总体研究。我们将其结果从经典Schrödinger方程的情况扩展到包括分数阶Schrödinger方程的一类方程。为此，我们完全避免了时间本地化的论点，从而大大简化了他们的证明。