Pointwise convergence along a tangential curve for the fractional Schrödinger equation

Authors

  • Chu-Hee Cho Seoul National University, Department of Mathematical Sciences and RIM
  • Shobu Shiraki Saitama University, Graduate School of Science and Engineering, Department of Mathematics

Keywords:

Fractional Schrödinger equation, pointwise convergence, fractional dimension

Abstract

In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schrödinger 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 Schrödinger equation, which in itself contains a result due to Lee, Vargas and the first author, to the fractional Schrödinger equation. The proof is based on a decomposition argument without time localization, which has recently been introduced by the second author.

 

Section
Articles

Published

2021-08-19

How to Cite

Cho, C.-H., & Shiraki, S. (2021). Pointwise convergence along a tangential curve for the fractional Schrödinger equation. Annales Fennici Mathematici, 46(2), 993–1005. Retrieved from https://afm.journal.fi/article/view/110914