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Information × Registration Number 0302U001582, 0100U003348 , R & D reports Title Functional spaces and semigroups popup.stage_title Пуассонові однорідні простори і динамічні r - матриці. Напівгрупи когомологічної вимірності 1. Напівгрупа рядів по функціям Уолша Head Favorov S.Yu., Registration Date 27-03-2002 Organization Kharkov National University named after V.N.Karazin popup.description2 The objects of the research are Poisson homogeneous spaces, semigroups of cohomological dimension 1, zero sets of absolutely monotonous functions, the entire functions with positive factors and with the real zeros for their pieces of Taylor series, holomorphic almost periodic functions,smoothness under the operation of convolution, series on Walsh functions.The purpose of the work is development of new methods in the complex analysis and algebra, application them in the functional analysis and theory of probabilities. Methods of the research are theoretical. During performance of work the connections between dynamic r-matrixes and Poisson homogeneous spaces of Poisson=Lee groups are found, the properties of ideals free semigroups which have cohomological dimension 1, are found, the indicators of the entire functions which are generating functions of multiple-positive functions of the finite order, are described, the conditions are established, under which all partial sums of Taylor series of the entire functions have only real zeros, the continuation of the property of almost periodicity of function from a strip to a tubular area is constructed, the conditions on a measure, sufficient for existence of the entire function with given the growth rate are received, which satisfies to an equation of convolution, at the certain restrictions the definiteness of series on Walsh functions by their module is proved. The obtained results are new, they were proved on seminars and conferences in Kiev, Kharkov, Sumy, St.-Petersburg, Tel Aviv, Haifa, Ber-Sheev, Manhattan (Kansas, USA), Aveiro (Portugal), Berlin, Szeged (Hungary), Nish (Yugoslavia). Assumptions concerning development of object research - applications of the offered constructions and received methods to topology, differential equations, theory of probabilities, the algebraic theory of numbers, radiophysics, computer science etc. Product Description popup.authors popup.nrat_date 2020-04-02 Close