论文标题
具有一般自相会边界条件的矩阵sturm-liouville操作员的直接和反向问题
Direct and inverse problems for the matrix Sturm-Liouville operator with the general self-adjoint boundary conditions
论文作者
论文摘要
矩阵sturm-liouville操作员在有限的间隔内，以一般的自我偶会形式的边界条件，并研究了$ w_2^{ - 1} $的奇异潜力。该操作员将Sturm-Liouville操作员概括为几何图。我们研究了该操作员的光谱数据（特征值和重量矩阵）的结构和渐近性能。此外，我们使用光谱映射方法证明了从其光谱数据中恢复运算符的独特性。
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators on geometrical graphs. We investigate structural and asymptotical properties of the spectral data (eigenvalues and weight matrices) of this operator. Furthermore, we prove the uniqueness of recovering the operator from its spectral data, by using the method of spectral mappings.
