Upper bounds for the approximation of certain classes of functions of a complex variable by Fourier series in the space \(L_2\) and \(n\)-widths

DOI10.1134/S0001434618030343zbMath1397.42001OpenAlexW2800633532MaRDI QIDQ722194

M. S. Saidusaynov, Mirgand Shabozovich Shabozov

Publication date: 23 July 2018

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434618030343

zbMATH Keywords

generalized modulus of continuityJackson-Stechkin inequalitymean-square approximationupper bounds for best approximations

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (5)

On the best simultaneous approximation of functions in the Bergman space \(B_2\) ⋮ Estimates of the values of \(n\)-widths of classes of analytic functions in the weight spaces \(H_{2,\gamma}(D)\) ⋮ Approximation of functions of a complex variable by Fourier sums in orthogonal systems in \(L_2\) ⋮ Sharp inequalities between the best root-mean-square approximations of analytic functions in the disk and some smoothness characteristics in the Bergman space ⋮ 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

• The exact constant in the Jackson inequality in \(L^ 2\)
• Jackson-Stechkin type inequalities for special moduli of continuity and widths of function classes in the space \(L_2\)
• Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes
• Best polynomial approximations in \(L_{2}\) of classes of \(2{\pi}\)-periodic functions and exact values of their widths
• Sharp estimates for the convergence rate of Fourier series of complex variable functions in L 2(D, p(z))
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