Spectral theory of some classes of singularly perturbed operators
Derkach Volodymyr Oleksandrovich,
Donetsk National University
A strong matrix moment problem and the truncated strong matrix moment problem are investigated. A sequence of two-point Pade approximants is constructed. A convergence of the sequence of two-point Pade approximants is studied. Convergence results for Pade approximants to some class of generalized Nevanlinna functions are obtained. A similarity of an indefinite Sturm-Liouville operator with decreasing potentials to a self-adjoint one is investigated. It is proved that the system of eigenfunctions and associated functions of a Sturm-Liouville operator with non-regular nondegenerate boundary conditions is not uniformly minimal. For a Dirac type differential operators with special boundary conditions the system of eigenfunctions and associated functions is shown to be complete, but do not form a basis.