Pointwise Convergence along non-tangential direction for the Schrodinger equation with Complex Time

被引：3
|
作者：
Yuan, Jiye [1 ]
Zhao, Tengfei [2 ]
Zheng, Jiqiang [3 ]
机构：
[1] China Acad Engn Phys, Grad Sch, POB 2101, Beijing 100088, Peoples R China
[2] Beijing Computat Sci Res Ctr, 10 West Dongbeiwang Rd, Beijing 100193, Peoples R China
[3] Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China
来源：
REVISTA MATEMATICA COMPLUTENSE | 2021年 / 34卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Pointwise convergence; Fractional Schrodinger operator; Maximal estimate; MAXIMAL OPERATORS;
D O I：
10.1007/s13163-020-00364-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the pointwise convergence to the initial data in a cone region for the fractional Schrodinger operator P-a,gamma(t) with complex time. By stationary phase analysis, we establish the maximal estimate for P-a,gamma(t) in a cone region. As a consequence of the maximal estimate, the pointwise convergence holds through a standard argument. Our results extend those obtained by Cho-Lee-Vargas (J Fourier Anal Appl 18:972-994, 2012) and Shiraki (arXiv:1903.02356v1) from the real value time to the complex value time.
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页码：389 / 407
页数：19
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