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Information × Registration Number 0221U102507, 0116U003102 , R & D reports Title Approximation characteristics and structural properties of functional sets popup.stage_title Head Romaniuk Anatolii S., Доктор фізико-математичних наук Registration Date 04-02-2021 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Object of investigation – linear spaces and approximative systems, functional sets. Aim of the work – developing methods for an effective apparatus of solving a number of important problems of the function theory, in particular, those that are connected to the approximation of the classes of functions of one and many variables, as well as the classes of analytic functions of complex variable. Method of investigation – methods of function theory and functional analysis. Within the scientific research work “Approximation characteristics and structural properties of functional sets”, a large variety of topics is covered of the modern approximation theory. An apparatus is developed for an effective solving of significant tasks of the theory of functions, that are under investigation of specialists that work in Ukraine as well as throughout Europe and the whole world. In particular, deep structural, including differential properties of the classes of smooth periodic and non-periodic functions of one and several real variables, and also of complex-variable functions, that belong to the known in their applications in different areas of mathematics, normed Nikolskii-Besov, Sobolev, Stepanets, Hardi spaces, etc. It allowed to create new and develop the known methods of investigation for the problems of evaluating important characteristics of linear and non-linear approximation using the approximate aggregates built on different classical basis systems, e.g., trigonometric, multiple Haar system and others. Key words: Lebesque spaces, Nikolskii-Besov classes, widths, best approximation, bilinear approximation, Fourier operator, hyperbolic cross, convolution of functions, multiple Haar basis, Fourier-Haar sums, nonlinear approximation, best m-term approximation, interpolation polynomial, linear approximation method, holomorphic function, Taylor series, Poisson integral, Hardi spaces, Orlicz spaces. Product Description popup.authors Bakan Andrew G Vygovska Albina D. Derevyanko Nadiya V Pozharska Kateryna V. Romanyuk Viktor S Savchuk Viktor V. Serdyuk Anatolii S. Stasyuk Serhii A Stepaniuk Tetiana A. Shidlich Andrii L. Yanchenko Sergiy Ya. popup.nrat_date 2021-02-04 Close