On approximation methods generated by Bochner-Riesz kernels

DOI10.1007/s00041-007-9004-yzbMath1268.42002OpenAlexW2041701331MaRDI QIDQ939090

Konstantin V. Runovski, Hans-Juergen Schmeisser

Publication date: 21 August 2008

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-007-9004-y

zbMATH Keywords

Bochner-Riesz meansfamilies of operatorsnecessary and sufficient conditions of convergencerealizations and moduli of smoothness related to the Laplacian

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Trigonometric interpolation (42A15)

Related Items (10)

A characterization of the convergence in variation for the generalized sampling series ⋮ Approximation properties of the sampling Kantorovich operators: regularization, saturation, inverse results and Favard classes in \(L^p\)-spaces ⋮ Quantitative estimates for sampling type operators with respect to the Jordan variation ⋮ Sharp estimates of approximation of periodic functions in Hölder spaces ⋮ Moduli of smoothness related to the Laplace-operator ⋮ Generalized Sampling Approximation of Bivariate Signals: Rate of Pointwise Convergence ⋮ The max-product generalized sampling operators: convergence and quantitative estimates ⋮ Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions ⋮ Extension of saturation theorems for the sampling Kantorovich operators ⋮ Multiplicator type operators and approximation of periodic functions of one variable by trigonometric polynomials

Cites Work

• On Fejér and Bochner-Riesz means
• Averages and \(K\)-functionals related to the Laplacian
• Best approximation and \(K\)-functionals
• Realization and smoothness related to the Laplacian
• Moduli of smoothness and \(K\)-functionals in \(L_ p\), \(0<p<1\)
• The Segal algebra \(\mathbf S_0(\mathbb R^d)\) and norm summability of Fourier series and Fourier transforms
• A Measure of Smoothnes Related to the Laplacian
• Wiener amalgams and pointwise summability of Fourier transforms and Fourier series
• ON THE MEAN INVERSION OF FOURIER AND HANKEL TRANSFORMS
• On the method of approximation by families of linear polynomial operators
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