Direct and Inverse Problems for the Matrix Sturm–Liouville Operator with General Self-Adjoint Boundary Conditions

The matrix Sturm–Liouville operator on a finite interval with boundary conditions in the general self-adjoint form and with singular potential of 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.