论文标题
在边界条件下分析功能的反向Sturm-Liouville问题
Inverse Sturm-Liouville problem with analytical functions in the boundary condition
论文作者
论文摘要
研究了在一个边界条件之一中具有复杂值的电位和任意整个功能的Sturm-Liouville操作员的逆频谱问题。我们获得了独特性的必要条件，并为反问题解决方案开发了建设性算法。主要结果应用于Hochstadt-Lieberman的半偏问题。作为辅助命题，我们证明了非自由选择案例中的cauchy数据证明了局部的溶解度和稳定性。
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.
