Móricz, F.; Siddiqi, A. H. Approximation by Nörlund means of Walsh-Fourier series. (English) Zbl 0757.42009 J. Approximation Theory 70, No. 3, 375-389 (1992). The authors prove under reasonable assumptions that the Nörlund kernel is quasi-positive. They use this to study the rate of approximation by Nörlund means for Walsh-Fourier series of a function in \(L^ p\) or \(\text{Lip}(\alpha,p)\) for \(\alpha>0\) and \(1\leq p\leq\infty\). These results generalize earlier work on Cesàro means by Yano, Jastrebova, and Skvortsov. This paper is very well written and contains two open problems near the end. Reviewer: W.R.Wade (Knoxville) Cited in 5 ReviewsCited in 33 Documents MSC: 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) Keywords:Lipschitz spaces; Sidon type inequality; rate of approximation by Nörlund means for Walsh-Fourier series; Cesàro means PDFBibTeX XMLCite \textit{F. Móricz} and \textit{A. H. Siddiqi}, J. Approx. Theory 70, No. 3, 375--389 (1992; Zbl 0757.42009) Full Text: DOI References: [1] Jastrebova, M. A., On approximation of functions satisfying the Lipschitz condition by arithmetic means of their Walsh-Fourier series, Mat. Sb., 71, 214-226 (1966), [Russian] · Zbl 0191.36802 [2] Moore, C. N., Summable Series and Convergence Factors, (American Mathematical Society Colloquium Publications, Vol. 22 (1938), Amer. Math. Soc: Amer. Math. Soc Providence, RI) · Zbl 0142.30704 [3] Móricz, F.; Schipp, F., On the integrability and \(L^1\)-convergence of Walsh series with coefficients of bounded variation, J. Math. Anal. Appl., 146, 99-109 (1990) · Zbl 0693.42023 [4] Paley, R. E.A. C., A remarkable system of orthogonal functions, (Proc. London Math. Soc., 34 (1932)), 241-279 · Zbl 0005.24901 [5] Schipp, F., On certain rearrangements of series with respect to the Walsh system, Mat. Zametki, 18, 193-201 (1975), [Russian] [6] Schipp, F.; Wade, W. R.; Simon, P., (Walsh Series. An Introduction to Dyadic Harmonic Analysis (1990), Akadémiai Kiadó: Akadémiai Kiadó Budapest) · Zbl 0727.42017 [7] Skvorcov, V. A., Certain estimates of approximation of functions by Cesàro means of Walsh-Fourier series, Mat. Zametki, 29, 539-547 (1981), [Russian] · Zbl 0467.42021 [8] Watari, C., Best approximation by Walsh polynomials, Tôhoku Math. J., 15, 1-5 (1963) · Zbl 0111.26502 [9] Yano, Sh, On Walsh series, Tôhoku Math. J., 3, 223-242 (1951) · Zbl 0044.07101 [10] Yano, Sh, On approximation by Walsh functions, (Proc. Amer. Math. Soc., 2 (1951)), 962-967 · Zbl 0044.07102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.