论文标题
矩阵Sturm-Liouville操作员的逆问题解决方案和光谱数据表征具有单数电位
Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential
论文作者
论文摘要
矩阵sturm-liouville操作员在有限的间隔内具有$ W_2^{ - 1} $的单数潜力，并研究了一般的自我接合边界条件。该操作员在几何图上概括了Sturm-Liouville操作员。我们研究了从光谱数据（特征值和权重矩阵）中恢复所考虑的运算符的逆问题。逆问题减少到合适的BANACH空间中的线性方程，并开发了逆问题解决方案的建设性算法。此外，我们获得了研究运算符的光谱数据表征。
The 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.
