Widths of some functional classes in the space \(L_2\) on a period

DOI10.1134/S0081543814090193zbMath1309.42001MaRDI QIDQ2514867

S. N. Vasil'ev

Publication date: 4 February 2015

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

weight functionmodulus of continuityJackson inequalitydifference operatorbest approximationwidth of functional class

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) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Trigonometric polynomials, inequalities, extremal problems (42A05)

Cites Work

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• Jackson inequality in \(L_{2}(\mathbb R^{N})\) with generalized modulus of continuity
• Widths in \(L_ 2\) of classes of differentiable functions, defined by higher-order moduli of continuity
• Sharp Jackson-Stechkin inequality in \(L_2\) with the modulus of continuity generated by an arbitrary finite-difference operator with constant coefficients
• Structural and constructive characteristics of functions in \(L_2\)
• Some inequalities between best approximations and moduli of continuity in an \(L_ 2 \)space
• Widths of classes from \(L_2[0,2\pi\) and minimization of exact constants in Jackson-type inequalities]
• Exact constants in Jackson-type inequalities and exact values of widths
• Best approximation of periodic functions by trigonometric polinomials in \(L_ 2\)
• DIAMETERS OF SETS IN FUNCTION SPACES AND THE THEORY OF BEST APPROXIMATIONS

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