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Information × Registration Number 0307U001653, 0106U003141 , R & D reports Title Algebraic and analytic methods of investigation of groups, classes of functions, operators and related objects popup.stage_title Тотожності та нерівності для норм операторів. Прості модулі з найстаршою вагою та еквіваріантне квантування Head Favorov U., Доктор фізико-математичних наук Registration Date 18-04-2007 Organization Kharkov National University named after V.N.Karazin popup.description2 The objects of the research are almost periodic holomorphic functions, polynomials with real zeros, modules over semisimple Lie algebras, generalized Daugavet property, convex combinations of positively defined functions, divisibility of elements of subsemigroups of topological algebras, non-commutative elementary semigroups. 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. During performance of work connections between simple highest-weight modules over semisimple Lie algebras and equivariant quantization were established; a class of Banakh spaces with generalized Daugavet property were investigated; the description of infinitely divisible elements of the semigroup of convex combinations of a topological algebra was given; the distribution of vaues of holomorphic almost periodic functions with the spectra in a cone was learned; the complete description of the set of normal divisors of convex linear combinations of positively defined functions is given;the class of linear operator that do not increase the number of real zeros was investigated; a non-commutative analogue of elementary semigroups is defined and studied. The obtained results are new, they were proved on seminars and conferences in Kiev, Kharkov, Lviv, St.-Petersburg, Odessa, Istanbul, Baltimore, Berlin. 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. ALMOST PERIODIC FUNCTIONS, TOPOLOGICAL ALGEBRAS, LIE ALGEBRAS, POSITIVELY DEFINED FUNCTIONS, REAL ZEROS OF POLYNOMIALS, DAUGAVET PROPERTY, ELEMENTARY SEMIGROUPS. 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