An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin \(L_2\)-inequality

DOI10.1134/S008154381502008XzbMath1344.42004OpenAlexW2006991702MaRDI QIDQ2516595

Dmitry Gorbachev

Publication date: 3 August 2015

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

Full work available at URL: https://doi.org/10.1134/s008154381502008x

zbMATH Keywords

trigonometric polynomialsbest approximationgeneralized modulus of continuityJackson-Stechkin inequality

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Best approximation, Chebyshev systems (41A50) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (3)

Delsarte’s extremal problem and packing on locally compact Abelian groups ⋮ Unnamed Item ⋮ On estimates in \(L_2(\mathbb{R} )\) of mean \(\nu \)-widths of classes of functions defined via the generalized modulus of continuity of \(\omega_\mathcal{M} \)

Cites Work

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• Jackson inequality in \(L_{2}(\mathbb T^{N})\) with generalized modulus of continuity
• Dunkl's theory and Jackson's theorem in the space \(L_2(\mathbb R^d)\) with power weight
• Jackson inequality in \(L_{2}(\mathbb R^{N})\) with generalized modulus of continuity
• Jackson's theorem in the space \(L_{2}(\mathbb R^{d})\) with power weight
• Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates
• Growth properties of Fourier transforms via moduli of continuity
• Multidimensional Jackson theorem in \(L_ 2\).
• Two related extremal problems for entire functions of several variables
• Optimal arguments in Jackson's inequality in the power-weighted space \(L_2(\mathbb R^d)\)
• An extremal problem for even positive definite entire functions of exponential type
• Best approximation of periodic functions by trigonometric polinomials in \(L_ 2\)
• Two external problems for trigonometric polynomials
• On Jackson's inequality for a generalized modulus of continuity in $ L_2$
• Extremum problems for entire functions of exponential spherical type

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