An inverse problem for a selfadjoint differential operator on the line

The inverse problem is considered for a high-order differential operator on the line. The inverse problem is formulated in terms of the Riemann problem. The data of the inverse problem arise as coefficients of the junction matrix of the Riemann problem. Under specific relations on the data of the inverse problem, which correspond to the self-adjointness of the original operator, the solvability of the Riemann problem is proved. The solution of the Riemann problem yields the solution of the inverse problem, as established in the paper.
Bibliography: 11 titles.