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：

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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。