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Approximation by Cesàro means of negative order of Walsh-Kaczmarz-Fourier series. (English) Zbl 1216.42006

Summary: We investigate the rate of approximation by Cesàro \((C,-\alpha)\)-means (where \(0<\alpha<1\)) of Walsh-Kaczmarz-Fourier series of a function in \(L^p\) \((1\leq p\leq\infty)\). In the case \(p=\infty\), by \(L^p\) we mean \(C_W\), the collection of uniformly \(W\)-continuous functions.
The approximation properties of Cesàro means of negative order of the Walsh-Fourier series were discussed earlier by U. Goginava [Bull. Georgian Acad. Sci. 166, No. 1, 20–22 (2002; Zbl 1096.42529)].

MSC:

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

Citations:

Zbl 1096.42529
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