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FUNCTIONAL-DIFFERENTIAL EQUATIONS IN HILBERT SPACE AND PROBLEM OF SPECTRAL THEORY CONNECTED WITH THEM

By Victor Valentinovich Vlasov and The Moscow Physical-Technical Institute (Russian Federation)

Abstract

The functional-differential equations (FDE) in the Hilbert space have been studied on base of the spectral analysis of the operator functions generated with these equations. The results about correct decision of the initial-boundary problems in the weighted Sobolev spaces on the semi-axis have been determined for wide class of the functional-differential equations (FDE) in the Hilbert space with unlimited operator coefficients and variable lags. The spectral analysis of the wide class operator beams with exponential occurance of the spectral parameter has been made. The Riesz basicity of the exponential solution system for neutral type FDE in the finite-dimensional space has been proven, and on this the accurate evaluations of the solutions in the critical and supercritical cases have been obtained. Usage field: theory of operator beams, theory of FDE, mathematical theory of control.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio

Topics: 12A - Pure mathematics, FUNCTIONAL-DIFFERENTIAL EQUATIONS, HILBERT SPACE, SPECTRAL THEORY
Year: 1997
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