Seminar "Inverse spectral problem for the matrix Sturm-Liouville operator"
Bondarenko Natalia Pavlovna — Doctor of Physical and Mathematical Sciences, SSU, Saratov.
The report is devoted to the matrix Sturm-Liouville operator on a finite interval with a singular potential and self-adjoint boundary conditions of a general form. This operator is a generalization of Sturm-Liouville operators on geometric graphs. An inverse problem will be considered, which consists in restoring the coefficients of the differential expression and boundary conditions from the spectral data (eigenvalues and weight matrices). The solution of the inverse problem is based on the development of the ideas of the method of spectral mappings. A characterization of the spectral data of the matrix operator will be given and its application to the Sturm-Liouville operator on a star graph will be shown.