Abstract The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness and develop a constructive algorithm for the inverse problem solution. The main results are applied to the Hochstadt-Lieberman half-inverse problem. As an auxiliary proposition, we prove local solvability and stability for the inverse Sturm-Liouville problem by the Cauchy data in the non-self-adjoint case.

中文翻译：

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边界条件下具有解析函数的逆 Sturm-Liouville 问题

摘要 研究了边界条件之一具有复值势和任意整函数的Sturm-Liouville算子的逆谱问题。我们获得了唯一性的充分必要条件，并为逆问题解决方案开发了一种构造算法。主要结果应用于 Hochstadt-Lieberman 半逆问题。作为辅助命题，我们通过非自伴随情况下的柯西数据证明了逆 Sturm-Liouville 问题的局部可解性和稳定性。