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Registration Number

0307U009135, 0106U008147 , R & D reports

Title

Spectral theory of some classes of singularly perturbed operators

Head

Derkach Volodymyr Oleksandrovich,

Registration Date

24-12-2007

Organization

Donetsk National University

Description

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.

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