Approximation of functions of a complex variable by Fourier sums in orthogonal systems in \(L_2\)

DOI10.3103/S1066369X20060080zbMath1462.41004OpenAlexW3047686451MaRDI QIDQ2225864

M. S. Saidusaynov, Mirgand Shabozovich Shabozov

Publication date: 11 February 2021

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

Full work available at URL: https://doi.org/10.3103/s1066369x20060080

zbMATH Keywords

generalized translation operatorJackson-Stechkin inequalityorthonormal system of functionsgeneralized module of continuity\(\mathcal{K}\)-functional

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Approximation in the complex plane (30E10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (2)

The best approximation and the values of the widths of some classes of analytical functions in the weighted Bergman space B_(2,γ) ⋮ 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

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• 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
• Weighted polynomial approximation
• K functionals and best polynomial approximation in weighted \(L^ p(R)\)
• 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
• K-FUNCTIONALS AND EXACT VALUES OF n-WIDTHS IN THE BERGMAN SPACE

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