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Pointwise Convergence along non-tangential direction for the Schrödinger equation with Complex Time
Revista Matemática Complutense ( IF 1.4 ) Pub Date : 2020-07-04 , DOI: 10.1007/s13163-020-00364-w
Jiye Yuan , Tengfei Zhao , Jiqiang Zheng

We study the pointwise convergence to the initial data in a cone region for the fractional Schrödinger operator \(P^{t}_{a,\gamma }\) with complex time. By stationary phase analysis, we establish the maximal estimate for \(P^{t}_{a,\gamma }\) 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.



中文翻译:

具有复时间的Schrödinger方程的非切向方向上的逐点收敛

我们研究了具有复杂时间的分数薛定ding算子\(P ^ {t} _ {a,\ gamma} \)在锥区域中初始数据的逐点收敛。通过平稳相位分析,我们建立了圆锥区域中\(P ^ {t} _ {a,\ gamma} \)的最大估计。作为最大估计的结果,通过标准自变量保持逐点收敛。我们的结果将Cho-Lee-Vargas(J Fourier Anal Appl 18:972-994,2012)和Shiraki(arXiv:1903.02356v1)获得的结果从实际价值时间扩展到了复杂价值时间。

更新日期:2020-07-05
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