The self-adjoint matrix Sturm–Liouville operator on a finite interval with singular potential of class \(W_2^{-1}\) and the general self-adjoint boundary conditions is studied. This operator generalizes the Sturm–Liouville operators on geometrical graphs. We investigate the inverse problem that consists in recovering the considered operator from the spectral data (eigenvalues and weight matrices). The inverse problem is reduced to a linear equation in a suitable Banach space, and a constructive algorithm for the inverse problem solution is developed. Moreover, we obtain the spectral data characterization for the studied operator. In addition, the main results are applied to the Sturm–Liouville operator on a graph of arbitrary geometrical structure.

研究了类\(W_2^{-1}\)奇异势有限区间上的自伴随矩阵Sturm-Liouville算子和一般自伴随边界条件。该算子在几何图形上推广了 Sturm-Liouville 算子。我们研究了从频谱数据（特征值和权重矩阵）中恢复所考虑的算子的逆问题。将逆问题简化为合适的 Banach 空间中的线性方程，并开发了用于逆问题求解的构造算法。此外，我们获得了所研究算子的光谱数据特征。此外，主要结果应用于任意几何结构图上的 Sturm-Liouville 算子。