In this paper, a class of inverse Sturm–Liouville problems of Atkinson type with transmission conditions is investigated. Based on the method of well-known theory for inverse matrix eigenvalue problems and the spectral properties of Sturm–Liouville problems with transmission conditions of Atkinson type, the corresponding Sturm–Liouville problems can be constructed using two sets of interlacing real numbers and some other conditions. We solve the problems not only under the separated boundary conditions, but also under the real coupled boundary conditions and the general real self-adjoint transmission conditions.

中文翻译：

---

具有透射条件的Sturm-Liouville问题的反谱问题

本文研究了一类带有传播条件的Atkinson型Sturm-Liouville逆问题。根据逆矩阵特征值问题的著名理论方法和具有Atkinson型传输条件的Sturm-Liouville问题的频谱性质，可以使用两组交织的实数和其他一些条件构造相应的Sturm-Liouville问题。我们不仅解决了分离边界条件下的问题，而且解决了实际耦合边界条件和一般的真实自伴传输条件下的问题。