On moduli of smoothness and averaged differences of fractional order

DOI10.1515/fca-2017-0051zbMath1371.26006arXiv1709.03168OpenAlexW2742663455MaRDI QIDQ2402336

Yurii S. Kolomoitsev

Publication date: 7 September 2017

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.03168

zbMATH Keywords

Fourier multipliersmodulus of smoothnessfractional orderaveraged differences

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Fractional derivatives and integrals (26A33) Other functions coming from differential, difference and integral equations (33E30) Multipliers in one variable harmonic analysis (42A45) Linear difference operators (47B39)

Related Items (5)

Unnamed Item ⋮ On generalized \(K\)-functionals in \(L_p\) for \(0<p<1\) ⋮ Sharp \(L_p\)-error estimates for sampling operators ⋮ On various moduli of smoothness and \(K\)-functionals ⋮ Properties of moduli of smoothness in \(L_p (\mathbb{R}^d)\)

Cites Work

• The Wiener algebra of absolutely convergent Fourier integrals: an overview
• Direct and converse theorems of the theory of approximation in the metric of \(L_p\) for \(0<p<1\)
• Moduli of smoothness and \(K\)-functionals in \(L_ p\), \(0<p<1\)
• On the nonclassical approximation method for periodic functions by trigonometric polynomials
• Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
• DIRECT AND CONVERSE THEOREMS OF JACKSON TYPE IN $ L^p$ SPACES, $ 0<p<1$
• Estimates of the best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the multidimensional Jackson's theorem
• Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $ H_p$, $ 0<p\le 1$
• The exact order of approximation to periodic functions by Bernstein-Stechkin polynomials
• Realization and characterization of modulus of smoothness in weighted Lebesgue spaces
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