Orydoroga L. On completeness of the root vector systems for some classes of ordinary differential operators

In the dissertation, we consider boundary value problems for nxn-systems of differential equations of the form 1/iBY’+Q(x)Y=lY. For these systems, we obtain sufficient conditions for the completeness of systems of eigenfunctions and associated functions. In case of the Dirac type 2x2-systems with splitting boundary conditions we prove not only the completeness but also the Riesz basis property for systems of eigenfunctions and associated functions, and for these systems we prove a theorem on the uniform equiconvergence with an expansion on eigenfunctions of the same boundary value problem for equation 1/iBY’=lY. In the 5th chapter of the dissertation we investigate boundary value problems for the fractional order differential equations. For these equations, we prove both an analogue of the Birkhoff theorem and a theorem on the completeness of root vectors of a boundary value problem in case of splitting boundary conditions.