Geodesic
Pointwise convergence along a tangential curve for the fractional Schrödinger equation
Chu-Hee Cho1 ; Shobu Shiraki2
1 Seoul National University, Department of Mathematical Sciences and RIM
2 Saitama University, Graduate School of Science and Engineering, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 993-1005.

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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.  
Keywords: Fractional Schrödinger equation, pointwise convergence, fractional dimension

Chu-Hee Cho 1 ; Shobu Shiraki 2

1 Seoul National University, Department of Mathematical Sciences and RIM
2 Saitama University, Graduate School of Science and Engineering, Department of Mathematics 
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Chu-Hee Cho; Shobu Shiraki. Pointwise convergence along a tangential curve for the fractional Schrödinger equation. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 993-1005. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a22/