Registration Number
0223U002840,
0120U102630
, R & D reports
Title
Extreme problems and methods of the theory of approximation of functional classes
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Head
Kharkevych Yuri І., Кандидат фізико-математичних наук
Registration Date
10-03-2023
Organization
Lesya Ukrainka Eastern European National University
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The project covers a wide range of issues of the modern theory of functions of a complex variable and the theory of polynomial and functional approximation, which provides for the possible practical implementation of the obtained scientific results in the field of mathematical programming. The main goal of scientific theoretical research is to develop effective methods for solving classical extremal problems of approximation theory on some important classes of analytic functions, classes of periodic functions of a real variable, as well as on classes of non-periodic functions of a real variable defined on the entire real axis. Both point estimates and estimates of Lebesgue norms with various weight functions for arbitrary algebraic polynomials of various domains of the complex plane are studied depending on the location of the point or the geometry of the domain.
The asymptotic characteristics of the Sobolev and Nikol'skii-Besov classes of periodic functions of several variables are studied. Estimates are established for the best approximations, approximations by Fourier sums and Zygmund sums of classes of periodic functions; asymptotic equalities are found for the exact upper bounds of approximations of functions differentiated in the sense of Stepanets by linear interpolation processes or linear methods of summation of Fourier series; ordinal estimates for the entropy numbers of the classes B^r_{p,\theta}, which are periodic functions of several variables in Lebesgue spaces, are established. Order-exact estimates for linear widths of generalized Nikol'skii-Besov classes of periodic functions of several variables in Lebesgue space are established.
Successful completion of the topic allows one to effectively solve problems classical for the theory of approximation of functions, allows one to find answers to important problems, and will give a significant impetus to the development of science and its practical application.
Product Description
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Borsuk Mykhailo M.
Hembarska Svitlana B.
Hembarskyi Mykhailo V.
Hrabova Uliana Z.
Zhyhallo Kostiantyn M.
Zhyhallo Tetiana V.
Kalchuk Inna V.
Piddubny Oleksii M.
Romanyuk Anatolii S.
Serdyuk Anatolii S.
Khanin Oleksandr H.
Kharkevich Yurii I.
Kharkevych Halyna I.
Shvai (Pozharska) Kateryna V.
Shvai Olha L.
Shutovsyi Arsen M.
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2023-03-10
