Geodesic
Pointwise convergence along a tangential curve for the fractional Schrödinger equation
Chu-Hee Cho1 ; Shobu Shiraki2
1Seoul National University, Department of Mathematical Sciences and RIM
2Saitama 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/