Constructive solution of the inverse spectral problem for the matrix Sturm–Liouville operator

Abstract

An inverse spectral problem is studied for the matrix Sturm–Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the considered inverse problem. The nonlinear inverse problem is reduced to a linear equation in a special Banach space of infinite matrix sequences. In addition, we apply our results to the Sturm–Liouville operator on a star-shaped graph.