Abstract We give a short review of results on inverse spectral problems for second-order differential operators on an interval with non-separated boundary conditions. We pay the main attention to the most important nonlinear inverse problems of recovering coefficients of differential operators from given spectral characteristics. In the first part of the review, we provide the main results and methods related to inverse problems for Sturm–Liouville operators with non-separated boundary conditions: periodic, quasi-periodic and Robin-type boundary conditions. At the end, we present the main results on inverse problems for differential pencils with non-separated boundary conditions.

中文翻译：

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具有非分离边界条件的微分算子的逆谱问题

摘要 我们简要回顾了具有非分离边界条件的区间上二阶微分算子的逆谱问题的结果。我们主要关注从给定谱特征恢复微分算子系数的最重要的非线性逆问题。在评论的第一部分，我们提供了与具有非分离边界条件的 Sturm-Liouville 算子的逆问题相关的主要结果和方法：周期、准周期和 Robin 型边界条件。最后，我们介绍了具有非分离边界条件的微分铅笔反问题的主要结果。