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 Cet article a éte moissonné depuis la source Journal.fi

Voir la notice de l'article

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 
@article{AFM_2021_46_2_a22,
     author = {Chu-Hee Cho and Shobu Shiraki},
     title = {Pointwise convergence along a tangential curve for the fractional {Schr\"odinger} equation},
     journal = {Annales Fennici Mathematici},
     pages = {993--1005},
     year = {2021},
     volume = {46},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a22/}
}
TY  - JOUR
AU  - Chu-Hee Cho
AU  - Shobu Shiraki
TI  - Pointwise convergence along a tangential curve for the fractional Schrödinger equation
JO  - Annales Fennici Mathematici
PY  - 2021
SP  - 993
EP  - 1005
VL  - 46
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a22/
LA  - en
ID  - AFM_2021_46_2_a22
ER  - 
%0 Journal Article
%A Chu-Hee Cho
%A Shobu Shiraki
%T Pointwise convergence along a tangential curve for the fractional Schrödinger equation
%J Annales Fennici Mathematici
%D 2021
%P 993-1005
%V 46
%N 2
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a22/
%G en
%F AFM_2021_46_2_a22
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/