On the best approximation in the mean of functions of a complex variable by Fourier series in the Bergman space

DOI10.3103/S1066369X20020073zbMath1443.41009OpenAlexW3006120267MaRDI QIDQ2191869

Kh. M. Khuromonov, Mirgand Shabozovich Shabozov

Publication date: 26 June 2020

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x20020073

zbMATH Keywords

\(n\)-widthssupremumJackson-Stechkin inequalitymodule of continuity\( \mathscr{K} \)-functional

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by polynomials (41A10) Convergence of Fourier series and of inverse transforms (43A50)

Related Items (2)

\(K\)-functionals and extreme problems of the approximation theory for classes of analytic functions in a circle. II ⋮ Exact inequalities between the best polynomial approximations and averaged norms of finite differences in the \(B_2\) space and widths of some classes of functions

Cites Work

• K functionals and best polynomial approximation in weighted \(L^ p(R)\)
• On the best approximation in the mean by algebraic polynomials with weight and the exact values of widths for the classes of functions
• Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes
• Sharp estimates for the convergence rate of Fourier series of complex variable functions in L 2(D, p(z))
• Mean-square approximation of complex variable functions by Fourier series in the weighted Bergman space
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