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Approximation by Nörlund means of Walsh-Kaczmarz-Fourier series. (English) Zbl 1210.42043

Summary: We study the rate of the approximation by Nörlund means of Walsh-Kaczmarz-Fourier series of a function in \(L^{p}\) \((1 \leq p \leq \infty )\). As a special case, we obtain the result due to V. A. Skvortsov [Anal. Math. 7, 141–150 (1981; Zbl 0472.42014)]. Earlier results on Walsh-Nörlund means were given by F. Móricz and A. H. Siddiqi [J. Approximation Theory 70, No. 3, 375–389 (1992; Zbl 0757.42009)].

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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