Approximation of functions by the Fourier-Walsh sums (Q580616)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Approximation of functions by the Fourier-Walsh sums |
scientific article; zbMATH DE number 4017550
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of functions by the Fourier-Walsh sums |
scientific article; zbMATH DE number 4017550 |
Statements
Approximation of functions by the Fourier-Walsh sums (English)
0 references
1987
0 references
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.
0 references
Dirichlet-Walsh kernel
0 references
