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Information × Registration Number 0214U000069, 0111U000482 , R & D reports Title Approximation, geometric and metric problems in the theory of functions and mappings popup.stage_title Head Ryazanov Vladimir Illich, Registration Date 15-01-2014 Organization Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine popup.description2 The short account of the main results: theorems of existence and representation of solutions of the general Beltrami equations with degeneration; convergence of the Fourier-Jacobi sums in spaces of functions that are integrable with weights; injectivity of the convolution operator; theorems on approximation of functions with linear combinations of shifts; the uniqueness theorem for functions with zero integrals over balls of a fixed radius; necessary and sufficient conditions of isotonic extension of mappings on partially odered sets; criteria of existence of multi-valued solutions of the Dirichlet problem for the degenerate Beltrami equations of the first kind in domains bounded by a finite number of mutually disjoint Jordan curves with the boundary functions admitting a countable set of points of discontinuity, in particular, with functions of bounded variation; extension of spatial mappings onto domains completed by prime ends; exact inequalities of the Ul'yanov type of various metrics for moduli of continuity in quasinormed spaces; exact order of growth of norms of integral strong mean spherical sums of Fourier for periodic functions of many variables; necessary and sufficient conditions of asymptotic homogeneity for families of regular solutions of the degenerate Beltrami equations with restrictions of the integral type for coefficient; resolution of the Riemann-Hilbert problem with measurable coefficients and measurable boundary dates; existence of solutions of the Riemann-Hilbert problem for the non-degenerate Beltrami equations of the first kind in quasidisks with coefficients of bounded variation and measurable boundary dates; lower estimates of moduli for homeomorphisms with finite distortion; analog of the Srebro-Vuorinen theorem on a continuous extension to the boundary of mappings with unbounded characteristic of quasiconformality and analogs of inequalities of the Vaisala-Poletski type for the modulus of the order p. Product Description popup.authors Афанасьєва Олена Сергіївна Волчков Валерій Володимирович Гутлянський Володимир Якович Довгоший Олексій Альфредович Ковтонюк Денис Олександрович Коломойцев Юрій Сергійович Кузнецова Ольга Іванівна Ломако Тетяна Володимирівна Моторний Віталій Павлович Очаковська Оксана Олександрівна Салімов Руслан Радікович Севостьянов Євген Олександрович popup.nrat_date 2020-04-02 Close