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Information × Registration Number 0218U001518, 0115U000481 , R & D reports Title Development of function-theoretic methods and applications in operator theory and mathematical statistics. popup.stage_title Head Favorov Sergii Yurijovich, Доктор фізико-математичних наук Registration Date 12-03-2018 Organization Kharkov National University named after V.N. Karazin popup.description2 Objects of research are analytic functions in the plane, subharmonic functions in the plane and a finite-dimensional space, their zero sets and Riesz measures, classes of irreducible elements and elements that do not have irreducible components, functions of Schur's class, scattering suboperators of unitary couplings, probability measures on cyclic groups, generating functions of infinitely logarithmic convex sequences, their zero sets, functions of the Laguerre-Polia class, formally generalized vector-valued functions, their convolutions, generalized Laurent series, their Fourier transformation, discrete measures in finite-dimensional space, hypercyclic operators, Banach spaces with the property of Daugavet. Methods of research are theoretical. The purpose of the research work is the development of new methods in complex analysis and their application in other sections of mathematics, in particular, in the theory of operators in Hilbert and Banach spaces, in mathematical statistics, in mathematical physics, etc. We find exact conditions between the growth of a subharmonic or an analytic function in a neighborhood of a compact set in a finite-dimensional space and the growth of their Riesz' measures. The classes of irreducible elements and elements that do not have irreducible components in the multiplicative semigroup of mixtures of normal distributions by the dispersion parameter are studied. New quantitative criteria for pseudo-extension of functions of the Schur class and their applications are obtained. We find descriptions of zero sets of generating functions of infinite logarithmically concave sequences. We investigate when entire functions and power series belong to the Laguerre-Polia class. We introduce and study the properties of a new convolution operation of operator-valued and vector-valued formal generalized functions, and apply it to construct fundamental solutions of linear differential equations in vector spaces over an arbitrary field of zero characteristic. The quasi-triangular structures of Lie bialgebras on semisimple Lie algebras over algebraically non-closed fields (in particular, over the field of formal Laurent series) are classified. A complete description of all measures in certain groups that have a trivial equivalence class is found. Sufficient conditions that the Fourier quasicrystal support is a subset of the union of finite number of lattices are found. Various properties of linear operators in a Banach space are transferred to nonlinear operators with the Lipschitz condition. The obtained scientific results fully correspond to the modern level of development of the corresponding branches of mathematics. They were published in world-class professional journals, in particular, Proceedings of the American Mathematical Society, Journal of Mathematical Analysis and Applications, Banach Journal of Mathematical Analysis, Journal of Mathematical Physics, Communications in Mathematical Physics, etc. The results obtained were tested at seminars and conferences in Kharkiv, Kyiv, Lviv, Chernivtsi, Ivano-Frankivsk (Ukraine), Murcia, Cartagenae (Spain), Gyeongju (Korea). The results obtained are fundamental and are widely used in other scientific disciplines - in topology, differential equations, radiophysics, physics, computer science, etc. The obtained results will be of interest to the relevant scientific and educational institutions (Kyiv and Lviv Universities, the Institute of Mathematics of the National Academy of Sciences of Ukraine, the mathematical department of the Institute of Physics and Mathematics of the National Academy of Sciences of Ukraine, etc.). Product Description popup.authors Є. Каролінський І. Ільїнська В. Дубовой В. Кадець В. Татанова Г. Вишнякова Л. Полякова Н. Александровська О. Ільїнський С. Гефтер popup.nrat_date 2020-04-02 Close