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Approximation of functions by the Fourier-Walsh sums. (English. Russian original) Zbl 0626.42003
Math. Notes 41, 15-22 (1987); translation from Mat. Zametki 41, No. 1, 23-33 (1987).
The author proves the following theorem: Let X be the space \(L^ 1[0,1]\) or \(L^{\infty}[0,1]\). Then for every natural number \[ \sup_{f\in X_{\epsilon}}\| f-S_ N(f)\|_ x\epsilon_ N+\sum^{N}_{n=1}\epsilon_{N+n}\int^{1/n}_{1/(n+1)}| D_ N(x)| dx, \] where \(D_ N(x)\) is the Dirichlet-Walsh kernel. In the trigonometric case equivalent results were obtained by the author and K. I. Oskolkov.
Reviewer: R.Gajewski
42A10 Trigonometric approximation
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Full Text: DOI
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