Best approximations of periodic functions of several variables from the classes \(B_{p,\theta}^{\Omega}\)

DOI10.1134/S000143461001013XzbMath1200.41030OpenAlexW2021828388MaRDI QIDQ1957020

Sergei A. Stasyuk

Publication date: 24 September 2010

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

Full work available at URL: https://doi.org/10.1134/s000143461001013x

zbMATH Keywords

modulus of continuitylevel surfaceHölder's inequalitytrigonometric polynomialVallée-Poussin kernelBari-Stechkin conditionperiodic function of several variablesstep hyperbolic cross

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) General harmonic expansions, frames (42C15)

Related Items (6)

Approximation of functions from Nikolskii-Besov type classes of generalized mixed smoothness ⋮ Constructive sparse trigonometric approximations for the functions with generalized mixed smoothness ⋮ On orders of approximation functions of generalized smoothness in Lorentz spaces ⋮ Estimates of approximative characteristics of the classes \(B_{p,\theta}^\Omega\) of periodic functions of many variables with given majorant of mixed continuity moduli in the space \(L_\infty\) ⋮ Order estimates for the approximating characteristics of functions from the classes \(S_{p,\theta}^\Omega B(\mathbb{R}^d)\) with a given majorant of mixed modules of continuity in the uniform metric ⋮ Estimates of approximative characteristics of the classes $B^{\Omega}_{p,\theta}$ of periodic functions of several variables with given majorant of mixed moduli of continuity in the space $L_{q}$

Cites Work

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• Approximation of the Besov classes of periodic functions of several variables in the space \(L_ q\)
• Representation and approximation of periodic functions of several variables with given mixed modulus of continuity
• On approximation and characterization of periodic multivariate functions which have a majorant of the mixed moduli of continuity of specific kind
• Approximation of multidimensional functions with a given majorant of mixed moduli of continuity
• Approximation characteristics of the classes B p,θ Ω of periodic functions of many variables
• DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
• Best Approximations and Kolmogorov and Trigonometric Widths of the Classes B Ω p,θ of Periodic Functions of Many Variables

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