On Nikol'skii inequalities for domains in \({\mathbb {R}}^d\)

DOI10.1007/s00365-016-9335-5zbMath1351.41007arXiv1409.5397OpenAlexW309030724MaRDI QIDQ530574

Z. Ditzian, Andriy Prymak

Publication date: 10 August 2016

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5397

zbMATH Keywords

Christoffel functionconvex domainsNikol'skii inequality

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Approximation by polynomials (41A10) Real polynomials: analytic properties, etc. (26C05)

Related Items (17)

𝐿^{𝑝}-Bernstein inequalities on 𝐶²-domains and applications to discretization ⋮ Sampling discretization and related problems ⋮ Problems and conjectures in approximation that I would like settled ⋮ Optimal sampling and Christoffel functions on general domains ⋮ Sampling discretization of integral norms and its application ⋮ Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions ⋮ Sharp constants of approximation theory. IV: Asymptotic relations in general settings ⋮ Nikol'skii inequalities for Lorentz-Zygmund spaces ⋮ Upper estimates of Christoffel function on convex domains ⋮ Geometric computation of Christoffel functions on planar convex domains ⋮ Relating coefficients of expansion of a function to its norm ⋮ Sharp constants of approximation theory. III. Certain polynomial inequalities of different metrics on convex sets ⋮ Nikol'skii-type inequalities for trigonometric polynomials for Lorentz-Zygmund spaces ⋮ Tchakaloff polynomial meshes ⋮ Nikol'skii-type inequalities for entire functions of exponential type in Lorentz-Zygmund spaces ⋮ Randomized weakly admissible meshes ⋮ Sharp constants of approximation theory. VI: weighted polynomial inequalities of different metrics on the multidimensional cube and ball

Cites Work

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• Nikol'skii inequalities for Lorentz spaces
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• New moduli of smoothness on the unit ball, applications and computability
• Convex Polynomial Approximation in the Uniform Norm: Conclusion
• Nikolskii-type inequalities for shift invariant function spaces
• Christoffel functions on curves and domains
• On Remez-type inequalities for polynomials in \(\mathbb R^m\) and \(\mathbb C^m\)

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