We consider the Schrödinger operator on a finite interval with an $L^1$-potential. We prove that the potential can be uniquely recovered from one spectrum and subsets of another spectrum and point masses of the spectral measure (or norming constants) corresponding to the first spectrum. We also solve this Borg–Marchenko-type problem under some conditions on two spectra, when missing part of the second spectrum and known point masses of the spectral measure have different index sets.

中文翻译：

---

Schrödinger算子的反谱问题中的混合数据

我们考虑具有$ L ^ 1 $势的有限区间上的Schrödinger算子。我们证明，可以从一个光谱和另一个光谱的子集以及对应于第一个光谱的光谱度量（或规范常数）的点质量中唯一地恢复电势。当第二个光谱的缺失部分和已知的光谱测量点质量具有不同的指标集时，我们还可以在某些条件下在两个光谱上解决此Borg–Marchenko型问题。