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Information × Registration Number 0213U002483, 0110U001365 , R & D reports Title Asymptotic methods of investigation of harmonic and analytic functions, represented by random series, Laplace-Stieltjes integrals and their generalizations popup.stage_title Head Skaskiv Oleh Bogdanovych, Registration Date 29-01-2013 Organization Ivan Franko National University of Lviv popup.description2 For analytic functions in the unit disk we established new estimates for exceptional sets in direct analogues of classical Wiman inequality and establish the Levy type effect in a class of random analytic functions. We establish relations between the growth of the maximal term of a Dirichlet series and its coefficients in terms of power and exponential asymptotics. We investigated the growth of integrals Poisson-Stieltjes in polidisk and half-plane. For entire multiple Dirichlet series and integrals of Laplace-Stieljes we found new description of exceptional sets in asymptotic relations in Wiman-Valiron theory. We established precise conditions on the measure and construct the Laplace-Stieljes type integral dependent on a small parameter in which the modulus of the integral does not exceed the maximum modulus integrand outside exceptional sets. Stability criterion is established for multiple Dirichlet series and Taylor-Dirichlet type series. We obtained conditions under which an analytic function and its Gelfond-Leontiev derivatives belong to the same class of convergence and investigated properties of Hadamar compositions of the Gelfond-Leontiev derivatives . We investigated convexity, close to convexity of entire solutions of linear differential equations with polynomial coefficients and obtained sufficient conditions for convexity and close to convexity of analytic functions in the unit disk with n-membered recurrence formula for their Taylor coefficients. We constructed the theory of analytic curves of bounded L-index, and obtained theorems of the localization of zeros of such curves. For Cesare polynomials of second degree and third degree we proved the S. Robinson hypothesis. Product Description popup.authors Бордуляк Марта Тимофіївна Задорожна Ольга Юліанівна Магола Ярослав Стефанович Скасків Олег Богданович Сумик Оксана Маркіянівна Трухан Юрій Степанович Фединяк Степан Іванович Чижиков Ігор Ельбертович Шаповаловська Людмила Олександрівна Шеремета Мирослав Миколайович popup.nrat_date 2020-04-02 Close