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Information × Registration Number 0214U003253, 0111U002152 , R & D reports Title Research of properties of delta-subharmonic and meromorphic functions, Fourier series popup.stage_title Head Malyutin Konstantin Gennadyevich, Registration Date 27-01-2014 Organization Sumy State University popup.description2 Object of research: subharmonic in the complex plane functions; subharmonic in the upper half-plane functions; analytic functions of zero order; multi-valued mapping. Objective of research: the study the properties of subharmonic in the upper half-plane functions and the distribution of their Riesz measures and full measures; the solution of interpolation problems in classes of analytic functions of zero order, the study of fixed points of multi-valued mappings. The method of investigation: method of Fourier series and variety methods of complex variable theory, the theory of subharmonic functions, methods of mathematical analysis and some methods from works of L. Rubel , A. Kondratyuk, A. Grishin , K. Malyutin, M. Krasnosel'skii and K. Soltanov. The main results. A theorem on the regularity of the growth of the Fourier coefficients of delta -subharmonic and meromorphic functions of completely regular growth in the half-plane is obtained. This theorem is analogous to the well-known theorem of A. Kondratyuk on meromorphic functions of completely regular growth in the plane. The theorem on accessory of indicator of delta-subharmonic and meromorphic functions of completely regular growth in the half-plane to the class Lp is obtained. The necessary and sufficient conditions for the solvability of interpolation problems in classes of entire functions and analytic in the upper half-plane functions of the order zero and normal type. These conditions are formulated in terms of the canonical products of interpolation nodes and in terms of measures defined by these nodes. The criteria of accessory of delta -subharmonic functions in the half-plane to the class of functions of finite gamma-epsilon growth are obtained. These criteria are formulated in terms of the Fourier coefficients of these functions. For gamma-admissible measure in the upper half-plane, the notion of canonical function are introduced. This notion is a generalization of canonical product Nevanlinna of analytic in half-plane functions of finite order. It is shown that for the growth function, which is defined in terms of Boutroue proximate order, permission definition and Nevanlinna canonical product coincide. A theorem on the lower order of subharmonic functions in the upper half-plane of infinite order with the full measure distributed on the imaginary axis is proved. A theorem on the image of a compact subset, satisfying "the acute angle", of a multi-valued mapping of the Euclidean space is proved.5481 Product Description popup.authors Багдасарян Артем Анатолійович Бобрун Світлана Євстахіївна Боженко Оксана Анатоліївна Ганнов Володимир Сергійович Зелінський Юрій Борисович Козлова Ірина Іванівна Малютін Олександр Костянтинович Матвійчук Сергій Вячеславович Одарченко Наталія Іванівна Руденко Роман Олександрович popup.nrat_date 2020-04-02 Close