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arXiv · 2006.03272

Pointwise convergence along a tangential curve for the fractional Schr\"odinger equation

Chu-hee Cho·Shobu Shiraki
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Abstract

In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schr\"odinger equations in one spatial dimension and estimate the capacitary dimension of the divergence set. We extend a prior paper by Lee and the first author for the classical Schr\"odinger equation, which in itself contains a result due to Lee, Vargas and the first author, to the fractional Schr\"odinger equation. The proof is based on a decomposition argument without time localization, which has recently been introduced by the second author.

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Chu-hee Cho, Shobu Shiraki. 2020-06-05. Pointwise convergence along a tangential curve for the fractional Schr\"odinger equation. https://arxiv.org/abs/2006.03272

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