Approximate properties of the root functions generated by the correctly solvable boundary value problems for higher order ordinary differential equations

In this work properties of systems of root functions generated by the correctly solvable boundary value problems for higher order ordinary differential equations are studied. The biorthogonal systems of functions corresponding to the system of root functions are constructed. The resulting systems of root functions are minimal systems. The completeness of systems of root functions in $L_2(0,1)$ is proved. The algorithm for the inverse problem is given by reconstruction of the boundary functions. Moreover, some identities are found for the eigenvalues of the considered operator.