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Information × Registration Number 0212U002063, 0109U000613 , R & D reports Title Investigations in homology algebra and function theory popup.stage_title Head Favorov Sergej, Доктор фізико-математичних наук Registration Date 18-01-2012 Organization Kharkov National University named after V.N. Karazin popup.description2 The object of researches includes analytic and subharmonic functions, cut-off of convex sets, in Banach spaces, transforms in the spaces of analytic functions, Gaussian divisors of probability distributions, 0-homology of semigroups, Poisson homogeneous spaces The purpose of the work - the development of new methods in the complex analysis and algebra and applying these methods to the functional analysis, theory of probabilities and mathematical statistics. Methods of research - theoretical. While doing the work we find Blaschke-type condition for zeros of analytic functions and Riesz measures of subharmonic functions in discs that increase near the parts of the circle, the condition depends of a thickness of the part; investigate connection of geometry of cut-offs of convex sets with Radon-Nikodym property, Daugavet property, and other properties of Banach spaces; investigate linear transforms of analytic functions that do not increase number of zeros in some domains; construct the example of probability distribution without Gaussian components such that any linear combination of random variables with this distribution has Gaussian component; quantize in explicit form reduced Poisson homogeneous spaces of a group with standard Drinfeld-Jimbo structure; construct the theory of 0-homology for semigroups and show its application for computation of the Eilenberg-Maklein homologies. The results obtained are new, they were approved at seminars and conferences in Kharkov, Kiev, Lvov, Odessa, Istanbul, Vroclaw, St.-Petersburg, Stockholm, Grenada, Hong Kong, Krakow, Toronto, Berlin, Joensuu. The expectations about development of research object are: the search of applications of the suggested constructions and methods obtained to topology, differential equations, probability theory, mathematical statistics, radiophysics, computer science etc. ANALYTIC FUNCTIONS, ZEROS OF ANALYTIC FUNCTIONS, CONVEX SETS, SUBHARMONIC FUNCTIONS, BANACH SPACE, PROBABILITY DISTRIBUTION, GAUSSIAN COMPONENTS, RIESZ MEASURE, POISSON HOMOGENEOUS SPACE, HOMOLOGY OF SEMIGROUPS. Product Description popup.authors Ільїнська І. Ільїнський О Александровська Н. Босенко Т. Вішнякова Г. Гиря Н. Кадець М. Каролінський Є Каткова О. Новіков Б. Полякова Л. Радченко Л. Хрипченко М. popup.nrat_date 2020-04-02 Close