In this paper, we consider the spectral problem for a Stieltjes string with both ends fixed and with one-dimensional damping at an interior point. We solve an inverse problem of recovering parameters of the Stieltjes string using partial information on the string and partial information on the spectrum. First we prove uniqueness and give an algorithm of recovering the unknown parameters of the string by virtue of a finite number of distinct not pure imaginary complex eigenvalues and a certain even number of real eigenvalues. For the case where only complex eigenvalues are used we solve the existence problem, i.e. propose conditions on a set of complex numbers necessary and sufficient for these numbers to be a subset of the spectrum of the problem.

中文翻译：

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内点阻尼 Stieltjes 弦的反问题

在本文中，我们考虑两端固定且在内点具有一维阻尼的 Stieltjes 弦的谱问题。我们使用字符串的部分信息和频谱的部分信息来解决恢复 Stieltjes 字符串参数的逆问题。首先，我们证明了唯一性，并给出了一种利用有限个不同的非纯虚复特征值和一定偶数个实特征值来恢复字符串未知参数的算法。对于仅使用复数特征值的情况，我们解决了存在性问题，即在一组复数上提出条件，这些复数是问题频谱的一个子集。