Pointwise Convergence Along Restricted Directions for the Fractional Schrödinger Equation

被引：0
作者：
Shobu Shiraki
机构：
[1] Saitama University,Department of Mathematics, Graduate School of Science and Engineering
来源：
Journal of Fourier Analysis and Applications | 2020年 / 26卷
关键词：
Fractional schrödinger equation; Pointwise convergence; 35Q41;
D O I：
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摘要：
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.
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