We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account.

中文翻译：

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非自伴Sturm–Liouville算子的反问题的局部可解性和稳定性

我们考虑有限区间上的非自伴Sturm–Liouville算子。研究了反频谱问题，这包括从其特征值和广义权数中恢复该算子。我们依靠频谱映射的方法证明了该反问题的局部可解性和稳定性。考虑了多个特征值的可能分割。