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.
引用
收藏
页码：389 / 407
页数：19
相关论文
共 50 条
  • [31] On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrodinger equation
    Antoine, X.
    Lorin, E.
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 354 : 15 - 30
  • [32] TIME RECURRENT BEHAVIOR IN THE NON-LINEAR SCHRODINGER-EQUATION
    ROWLANDS, G
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (07): : 2395 - 2399
  • [33] Time-dependent Schrodinger equation with non-central potentials
    Ferkous, N.
    Bounames, A.
    Maamache, M.
    PHYSICA SCRIPTA, 2013, 88 (03)
  • [34] LONG TIME DYNAMICS FOR THE ONE DIMENSIONAL NON LINEAR SCHRODINGER EQUATION
    Burq, Nicolas
    Thomann, Laurent
    Tzvetkov, Nikolay
    ANNALES DE L INSTITUT FOURIER, 2013, 63 (06) : 2137 - 2198
  • [35] Large time behavior of solutions to Schrodinger equation with complex-valued potential
    Aafarani, Maha
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2021, 150 : 64 - 111
  • [36] Solution of the time-dependent Schrodinger equation using uniform complex scaling
    Bengtsson, Jakob
    Lindroth, Eva
    Selsto, Solve
    PHYSICAL REVIEW A, 2008, 78 (03):
  • [37] THE FRACTIONAL COMPLEX TRANSFORM: A NOVEL APPROACH TO THE TIME-FRACTIONAL SCHRoDINGER EQUATION
    Ain, Qura Tul
    He, Ji-Huan
    Anjum, Naveed
    Ali, Muhammad
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (07)
  • [38] WELL-POSEDNESS AND CONVERGENCE FOR TIME-SPACE FRACTIONAL STOCHASTIC SCHRODINGER-BBM EQUATION
    Wu, Shang
    Huang, Jianhua
    Li, Yuhong
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2021, 11 (04): : 1749 - 1767
  • [39] Dispersive hydrodynamics in non-Hermitian nonlinear Schrodinger equation with complex external potential
    Chandramouli, Sathyanarayanan
    Ossi, Nicholas
    Musslimani, Ziad H.
    Makris, Konstantinos G.
    NONLINEARITY, 2023, 36 (12) : 6798 - 6826
  • [40] Pointwise error estimate of an alternating direction implicit difference scheme for two-dimensional time-fractional diffusion equation
    Wang, Yue
    Chen, Hu
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 99 : 155 - 161
12345