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0210U001376,
0107U000937
,
Some problems of the theory of one-parametric operator semigroups in Hilbert and Banach space
Gubreev Gennady Michailovich,
10-02-2010
Polava National Technical University named in the honour of Yuri Kondratyuk
Object research: strongly continuous semigroups of operators in Hilbert and Banach spaces. Aim of SRW: finding the simple criteria of the fact that the inverse operator is finite-dimensional perturbations of Volterra operators (operators of class K) generates in Hilbert space C0-semigroup; building and research of functional models of operators of klass K in the case when finite-dimensional perturbations is built using the certain matrix weights of Mukenhaupt; solution of the problem of inverse operator to generator of uniform bounded semi-group; research of the growth of discrete semigroup which consists of the powers of transformation of Cayley generator of uniform bounded semigroup; to find the application to the solving of some problems of modern analisys etc. The method of research is based on integral estimation of norms of resolvent, on the technique of Muckenhoupt matrix-weights and functional models of nonselfadjoint operators; on integral representations of one-parametric semigroups of operators. In result of scientific and research work above-mentioned problems were solved. The obtained results are new and they can be used by the functional analysis specialists. Besides they can be put on the basement of special courses for students of mathematical specialities.
Гомілко Олександр Михайлович
Губреєв Геннадій Михайлович
Долгополова Марина Володимірівна
Лукашенко Галина Вікторівна
Недобачій Станісла Іванович
2020-04-02
Updated: 2025-12-08
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