Widths of some classes of functions defined by the generalized moduli of continuity \(\omega_\gamma\) in the space \(L_2\)

DOI10.1007/s10958-017-3577-zzbMath1381.42003OpenAlexW2761182005MaRDI QIDQ1683347

Sergei B. Vakarchuk

Publication date: 7 December 2017

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-017-3577-z

zbMATH Keywords

Fourier coefficientsbest polynomial approximation\(n\)-width

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (3)

Approximation by classical orthogonal polynomials with weight in spaces \(L_{2, \gamma }(a,b)\) and widths of some functional classes ⋮ On the estimates of the values of various widths of classes of functions of two variables in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp ( - x^2 - y^2)\) ⋮ On the estimates of widths of the classes of functions defined by the generalized moduli of continuity and majorants in the weighted space \(L_{2,x}(0, 1)\)

Cites Work

• Generalized smoothness characteristics in Jackson-type inequalities and widths of classes of functions in \(L_2\)
• Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions
• On the best polynomial approximation in the space \(L_2\) and widths of some classes of functions
• Widths in \(L_ 2\) of classes of differentiable functions, defined by higher-order moduli of continuity
• Jackson-type inequalities and widths of function classes in \(L_{2}\)
• A sharp inequality of Jackson-Stechkin type in \(L_{2}\) and the widths of functional classes
• Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi,\beta)\)-differentiable functions in \(L_2\). I
• Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi, \beta)\)-differentiable functions in \(L_2\). II
• On the best polynomial approximations in \(L_2\) of some classes of \(2\pi\)-periodic functions and of the exact values of their \(n\)-widths
• Jackson-Stechkin type inequalities for special moduli of continuity and widths of function classes in the space \(L_2\)
• Best Polynomial Approximations in L 2 and Widths of Some Classes of Functions
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