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Information × Registration Number 0200U003748, 0198U005531 , R & D reports Title Constructing of model representions of linear operators, spectral decomposition of curvers in Hilbert spaces and their applications in the theory of dynamic systems and the theory of stochastic functions. popup.stage_title Head Zolotar'ov V.A., Registration Date 12-09-2000 Organization Kharkov National University named after V.N.Karazin popup.description2 Subject of research - systems of linear operators which form Lie algebra and to study spectral representations for contractive operators in Hilbert spaces which are generated by the Bessel operator. Objective of research - to construct the systens of linear operators which form Lie algebra and to study spectral representations for contractive operators in Hilbert spaces which are generated by the Bessel operator. Methods - functional analysis, theory of functions and theory of differential operators. The functional model of Lie algebra for linear non-selfadjoint operators SL(2,R) has been constructed. Non-Abel sheme of Lax-Phillips scattering on the group SL(2,R) has been created. The corresponding analogue of spectral theory for the Jacobi five-diagonal matrices has been constructed. The important connections to the exponential momentum problem in the case when the measure is gathered on the cross RxR have been made. The explicit form of ortogonal quazipolinomials on this cross has been found. Multidimensional triangular models of operators which are unitary equivalent to integration operators on the independent variables in L (D), where D - is a domain in R with a piecewise linear boundary has been created. Product Description popup.authors popup.nrat_date 2020-04-03 Close