We consider the Sturm–Liouville operator on quantum graphs with a loop with the standard matching conditions in the internal vertex and the jump conditions at the boundary vertex. Given the potential on the loop, we try to recover the potential on the boundary edge from the subspectrum. The uniqueness theorem and a constructive algorithm for the solution of this partial inverse problem are provided.

中文翻译：

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带环量子图的局部逆问题

我们考虑量子图上的Sturm–Liouville算子，该算子具有内部顶点的标准匹配条件和边界顶点的跳跃条件的循环。给定回路上的电势，我们尝试从子频谱中恢复边界边缘上的电势。提供了唯一性定理和构造算法来解决该部分逆问题。