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Registration Number

0214U007991, 0112U001059 , R & D reports

Title

Creating and using of algebraic and functional methods.

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Head

Favorov Sergey, Доктор фізико-математичних наук

Registration Date

19-01-2015

Organization

Kharkov National University named after V.N. Karazin

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Objects of the research are mathematical models of quasicrystals, subharmonic functions in a ball, semigroups and their partial actions, Banach spaces, Lie bialgebras, hyperbolic polynomials, semistable distributions, oriented graphs. The purpose of the research is to develop new methods of analysis and algebra and applications of these methods in functional analysis and probability theory. Methods of the research are theoretical. Main results of the research are as follows: it is proved that every almost periodic Fourier quasicrystal of finite type is a finite union of shifts of the same lattice that gives a negative answer to the question of Lagarias; it is proved that if the set of zero differences of an exponential sum with purely imaginary exponents is a discrete set, then the zeros are periodic, and the exponential sum itself is the product of a finite number of sine shifts with the same period; Blaschke type conditions for the Riesz measure of subharmonic functions in a finite-dimensional ball that can grow when approaching a certain part of the boundary are found (the condition depends on the density of this part); the Radon-Nikodym theorem for multivalued maps is proved; the Tingley problem for finite-dimensional polyhedral spaces is solved; geometric properties of the cone of all polynomials that are non-negative on the real axis and has non-negative coefficients are studied; necessary and sufficient conditions for an entire function to belong to the Laguerre-P?lya class are found. The results of the research are new, they are approved at seminars and conferences in Kharkiv, Kyiv, Lviv, St. Petersburg, Ufa, Krakow, Toronto, Hong Kong, Sao Paulo, Florianopolis (Brazil), Santiago (Chile), Istanbul, Budapest, London, Edinburgh, Tel Aviv, Barcelona, Granada. Expectations on the further development of the research are to look for applications of the proposed structures and methods to probability theory, mathematical statistics, analytic number theory, topology, differential equations, quasicrystal theory, radio physics, computer science and so on.

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Ільїнський О.
Александровська Н.
Вишнякова Г.
Гиря Н.
Кадець В.
Каролінський Є.
Полякова Л.
Фаворов C.

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2020-04-02