On Gibbs-Wilbraham phenomenon and the arclength of Fourier series (Q636811)
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scientific article; zbMATH DE number 5944313
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Gibbs-Wilbraham phenomenon and the arclength of Fourier series |
scientific article; zbMATH DE number 5944313 |
Statements
On Gibbs-Wilbraham phenomenon and the arclength of Fourier series (English)
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30 August 2011
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The arclength of the graphs \(\Gamma (S_N(f))\) of the partial sums \(S_N(f)\) of the Fourier series of a piecewise \(C^1\) function \(f\) with jump discontinuities is asymptotically equal to (the sum of all jumps of \(f)\times L_N\), where \(L_N\) is the Lebesgue constant. This is an improvement of \textit{R. Strichartz} [J. Fourier Anal. Appl. 6, 533--536 (2000; Zbl 0967.42002)].
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Fourier series
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Gibbs-Wilbraham phenomenon
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arc length
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piecewise \(C ^{1}\) function
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Lebesgue constant
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