Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions

DOI10.1002/MANA.200810180zbMath1222.42005OpenAlexW2053390550MaRDI QIDQ3087903

Vladimir I. Rukasov, Konstantin V. Runovski, Hans-Juergen Schmeisser

Publication date: 17 August 2011

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.200810180

zbMATH Keywords

smoothness\(K\)-functionalsperiodic functionsrealization functionalsapproximation processesclassical kernelsfamilies of linear trigonometric polynomial operators

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Multipliers for harmonic analysis in several variables (42B15)

Related Items (10)

Approximation by Fourier means and generalized moduli of smoothness ⋮ Covering mappings in a product of metric spaces and boundary value problems for differential equations unsolved for the derivative ⋮ Quality of approximation by Fourier means in terms of general moduli of smoothness ⋮ Approximation by families of generalized sampling series, realizations of generalized \(\mathcal{K} \)-functionals and generalized moduli of smoothness ⋮ Periodic Besov spaces and generalized moduli of smoothness ⋮ Moduli of smoothness related to the Laplace-operator ⋮ Moduli of smoothness related to fractional Riesz-derivatives ⋮ Besov spaces with generalized smoothness and summability of multiple Fourier series ⋮ A direct theorem of approximation theory for a general modulus of smoothness ⋮ On controlling objects whose motion is defined by implicit nonlinear differential equations

Cites Work

• On Fejér and Bochner-Riesz means
• Computational aspects of a method of stochastic approximation
• On approximation methods generated by Bochner-Riesz kernels
• On convergence of families of linear polynomial operators
• Averages and \(K\)-functionals related to the Laplacian
• Realization and smoothness related to the Laplacian
• Moduli of smoothness and \(K\)-functionals in \(L_ p\), \(0<p<1\)
• On the method of approximation by families of linear polynomial operators
• On Jackson type inequality in Orlicz classes
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