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Approximation by Nörlund means of Walsh-Fourier series. (English) Zbl 0757.42009

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.

MSC:

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