On degree of approximation of function belonging to the Lipschitz class by \((C,1)(E,1)\) means of its Fourier series (Q2783538)
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scientific article; zbMATH DE number 1730545
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On degree of approximation of function belonging to the Lipschitz class by \((C,1)(E,1)\) means of its Fourier series |
scientific article; zbMATH DE number 1730545 |
Statements
9 February 2004
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summation of Fourier series
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degree of approximation
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Cesàro means
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Lipschitz class
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On degree of approximation of function belonging to the Lipschitz class by \((C,1)(E,1)\) means of its Fourier series (English)
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The authors prove the following estimate NEWLINE\[NEWLINE\|(CE)_n^1-f\|_{\infty}=\begin{cases} O\left(\frac{1}n^{\alpha}\right),& 0<\alpha<1, \\ O\left(\frac{\log n}{n}\right),&\alpha=1\end{cases} NEWLINE\]NEWLINE for any \(2\pi\)-periodic function \(f\in\) Lip \(\alpha\). (The notations are the same as in the following review [\textit{S. Lal}, Tamkang J. Math. 30, 47-52 (1999; Zbl 1032.42004)].
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