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Information × Registration Number 0217U001062, 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 01-02-2017 Organization Kharkov National University named after V.N. Karazin popup.description2 Research objects are analytic functions on the plane, subharmonic functions on the plane and on a finite-dimensional space, their null-sets and Riesz measures; classes of indecomposable elements and of elements possessing no indecomposable components, functions of Schur class, suboperators of unitary couplings scattering, probabilistic measures on cyclic groups. Research methods - theoretical. The aim of research is the development of new methods in complex analysis and their application in other branches of mathematics, in particular in operator theory (in Hilbert spaces and Banach spaces), in mathematical statistics, in mathematical physics, etc. Exact in some sense connections between the conditions of growth of subharmonic or analytic in a neighborhood of a compact subset of plane functions (for subharmonic functions -- also in a finite-dimensional space) and corresponding distribution of zero sets or Riesz measures are found. Also, connections between these conditions and various characteristics of the compact are studied. Effective quantitative criteria for pseudo-extensions of functions of Schur class are obtained, and factorization properties for suboperators of scattering of unitary couplings are found. Classification theorems for quasi-triangular structures of Lie bialgebras on semi-simple Lie algebras over algebraically incomplete fields (in particular over the field of formal Laurent series) are demonstrated. The complete description of all measures on some groups that have the trivial equivalence class (with respect to moduli of characteristic functions) is given. A new concept of fundamental solution for linear differential and difference-differential equation in a vector space is elaborated. Sufficient condition that ensure that an entire function belongs to the Laguerre-Polia class are found. The scientific results obtained in frames of this project are new, valuable and completely agree with the modern level of corresponding branches of contemporary mathematics. They are published in top-rank international scientific journals, in particular in 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 were reported on seminars and conferences in Khakiv, Kyiv, Lviv, Chernivtsi, Ivano-Frankivsk, Murcia, Cartagena (Spain), Gyeongju (Korea). The results are of fundamental nature and find various applications in other fields like topology, differential equations, radiophysics, physics, computer science, etc. They can be of interest for corresponding scientific groups in Kiev and Lviv Universities, Mathematical Institute of Ukrainian Academy of Sciences, Mathematical Division of Institute for Low Temperature Physics and Engineering and others. 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