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Registration Number

0214U007992, 0112U001060 , R & D reports

Title

Spectral analysis of operator systems and its applications

Head

Yantsevich Artem,

Registration Date

19-01-2015

Organization

Kharkov National University named after V.N. Karazin

Description

The object of research - systems of commutative operators and their model representations in multivariable domains on the plane. Operators that are kernel perturbations of differential operators. Non-stationary vector curves in a Hilbert space. Curves of finite range of non-stationarity. Systems of orthogonal polynomials on rays, non-stationary sequences, moment equalities, J-symmetrical and J-skew-symmetrical operators. The purpose of operation - construction of multidimensional triangular models for systems of non-selfadjoint operators. Solution of inverse problems for integro-differential operators. Construction of correlating and spectral theory of non-stationary vector curves in Hilbert spaces using models representations of operator systems. Solution of matrix trigonometric, Hausdorff truncated matrix, Stiltjes matrix, strong Hamburger matrix, strong Stiltjes matrix moment problems. Methods of research - functional analysis, theory of functions and theory of differential operators. Main results - multidimensional triangular models for systems of non-selfadjoint operators which are unitarily equivalent to the systems operators of integrations by independent variables. New methods of solution of direct and inverse problems of spectral analysis and problems of scattering for integro-differential operators. Description of the class of non-stationary vector curves of finite range of non-stationarity. Correlation and spectral theories of such curves. Solution of matrix trigonometric, truncated Hausdorff matrix, Stiltjes matrix, strong Hamburger matrix, strong Stiltjes matrix problems.

Product Description

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Загороднюк С.
Золотарьов В.
Когут Є.
Колтунов Й.
Розуменко О.
Янцевич А.