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Information × Registration Number 0209U006050, 0106U003141 , R & D reports Title Algebraic and analytic methods of investigation of groups, classes of functions, operators and related objects popup.stage_title Head Favorov U., Доктор фізико-математичних наук Registration Date 20-01-2009 Organization Kharkov National University named after V.N.Karazin popup.description2 The report on the research N 2-11-06: 54 pp., 56 sources. The objects of the research are normal meromorphic functions, polynomials with real zeros, modules over semisimple Lie algebras, generalized Daugavet property, partial projective representations of groups, cohomology of semigroups, zero sets of entire functions, Gaussian divisors of positively defined functions. The purpose of the work is development of new methods in the complex analysis and algebra, application of them in the functional analysis and theory of probabilities. Methods of the research are theoretical. Connections between simple highest-weight modules over semisimple Lie algebras and equivariant quantization were established; a class of Banach spaces with generalized Daugavet property were investigated; the complete zero sets of description of exponential entire functions was obtained; the complete description of the set of normal divisors of convex linear combinations of positively defined functions is given; various positivityconditions of real polynomials are investigated; differential operators of degree one that do not increase the number of real zeros was investigated; a notion of partial projective representation of groups is proposed, the Schur multiplier for that type of representations was built, and a connection with semigroups 0-cohomology was stated; a complete parametric description of the first category normal functions in the plane was obtained. The obtained results are new, they were proved on seminars and conferences in Kiev, Kharkov, Lviv, St.-Petersburg, Odessa, Istanbul, Stockholm, Berlin, Jounsuu, Grenada, Wroclaw. Assumptions concerning development of object research - the search of applications of offered constructions and received methods to topology, differential equations, theory of probabilities, mathematical statistics, algebraic theory of numbers, radio physics, computer sciences etc. NORMAL MEROMORPHIC FUNCTIONS, PROJECTIVE REPRESENTATIONS, LIE ALGEBRAS, SEMIGROUP COHOMOLOGY, SIMPLE MODULES, DAUGAVET OPERATORS, POSITIVE POLYNOMIALS, EXPONENTIAL TYPE FUNCTIONS, GAUSSIAN DIVISORS. Conditions of reception of the report: under the contract. 61077, Kharkov, Svobody sq., 4, Kharkov National University. Product Description popup.authors popup.nrat_date 2020-04-02 Close