The derivatives and integrals of fractional order in Walsh-Fourier analysis, with applications to approximation theory

DOI10.1016/0021-9045(83)90079-5zbMath0523.42022OpenAlexW1985206052MaRDI QIDQ584665

Zelin He

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0021-9045(83)90079-5

zbMATH Keywords

Bernstein theoremmeansdegree of approximationfractional orderWalsh-Fourier seriesfractional Jackson type theorem

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Rate of convergence, degree of approximation (41A25)

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General linear summation of the Vilenkin-Fourier series, Sidon-type inequalities and strong approximation by Fourier sums in multiplicative systems, On the order of approximation by Fejér means of Hermite-Fourier and Laguerre-Fourier series, Gibbs derivatives, Gibbs–butzer derivatives and their applications¹, The optimal dyadic derivative, On the order of approximation by Riesz means in multiplicative systems in the classes \(E_{X}[\varepsilon \)], Two-dimensional wave equations with fractal boundaries, Two-dimensional wave equations with fractal boundaries, Lipschitz classes on local fields, Modified dyadic integral and fractional derivative on \(\mathbb R_{+}\), A derivative on the field of \(p\)-adic numbers, Approximation of functions of bounded \(p\)-fluctuation by polynomials with respect to multiplicative systems, The \(p\)-adic differential-integral type operator, Unnamed Item

Cites Work

• Best approximation by Walsh polynomials
• Fractional differentiation on the group of integers of a \(p\)-adic or \(p\)-series field
• On a generalization of the concept of derivative
• Walsh-fourier series and the concept of a derivative^†
• On Approximation by Walsh Functions
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