Averages and \(K\)-functionals related to the Laplacian

DOI10.1006/jath.1997.3262zbMath0963.41010OpenAlexW2062804552MaRDI QIDQ1288269

Z. Ditzian, Konstantin V. Runovski

Publication date: 2 April 2001

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.1997.3262

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Rate of convergence, degree of approximation (41A25)

Related Items (11)

Some equivalence theorems with \(K\)-functionals ⋮ A note on the equivalences between the averages and the \(K\)-functionals related to the Laplacian ⋮ Convergence analysis for kernel-regularized online regression associated with an RRKHS ⋮ On approximation by reproducing kernel spaces in weighted \(L^p\) spaces ⋮ Multivariate approximating averages. ⋮ On approximation methods generated by Bochner-Riesz kernels ⋮ Characterizations of Besov and Triebel-Lizorkin spaces via averages on balls ⋮ The convergence rate for a \(K\)-functional in learning theory ⋮ Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions ⋮ Unnamed Item ⋮ Averages on caps of \(S^{d-1}\)

Cites Work

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• Best approximation and \(K\)-functionals
• The lower estimate for linear positive operators. I
• A Measure of Smoothnes Related to the Laplacian
• Approximation by Bernstein Polynomials
• Multivariate Landau–Kolmogorov-type inequality
• Strong converse inequalities

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