The Landau-Kolmogorov inequality revisited

DOI10.3934/dcds.2014.34.1183zbMath1280.41012arXiv1210.7708OpenAlexW2963404273MaRDI QIDQ379800

A. Yu. Shadrin

Publication date: 11 November 2013

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.7708

zbMATH Keywords

Landau-Kolmogorov inequalityexact constantsinequalities between derivativesZolotarev polynomials

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by polynomials (41A10) Numerical differentiation (65D25) Best constants in approximation theory (41A44)

Related Items (9)

An explicit radical parametrization of Zolotarev polynomials of degree 7 in terms of nested square roots ⋮ Reduction of the Kolmogorov inequality for a non negative part of the second derivative on the real line to the inequality for convex functions on an interval ⋮ The Landau-Kolmogorov problem on a finite interval in the Taikov case ⋮ Autour d'un probl\`eme extr\'emal \'etudi\'e par Edmund Landau ⋮ On the Largest Critical Value of $T_n^(k)$ ⋮ Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules ⋮ Landau-Kolmogorov type inequalities for curves on Riemannian manifolds ⋮ On the Landau-Kolmogorov inequality between $\| f' \|_{\infty}$, $\| f \|_{\infty}$ and $\| f \|_1$ ⋮ On modulus of continuity of differentiation operator on weighted Sobolev classes

Cites Work

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• The Landau inequality for bounded intervals with \(\| f^ 3\|\) finite
• Some extremal properties of perfect splines and the pointwise Landau problem on the finite interval
• Some best constants in the Landau inequality on a finite interval
• Error bounds for Lagrange interpolation
• Error formulas for divided difference expansions and numerical differentiation
• On a problem of I. Schur
• On inequalities between the maxima of the absolute values of a function and its derivatives on a half-line
• A Note on Landau's Problem for Bounded Intervals

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