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arXiv · 1903.02356

Pointwise convergence along restricted directions for the fractional Schr\"odinger equation

Shobu Shiraki
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Abstract

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

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Shobu Shiraki. 2019-03-06. Pointwise convergence along restricted directions for the fractional Schr\"odinger equation. https://arxiv.org/abs/1903.02356

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