On Gibbs-Wilbraham Phenomenon and the Arclength of Fourier Series |
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| Authors: | Kazuki Dempo Shigehiko Kuratsubo |
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| Affiliation: | 1. Department of Mathematical Sciences, Hirosaki University, Hirosaki, 036-8561, Japan
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| Abstract: | The arclength of the graphs Γ(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 equal asymptotically to $(hbox{the sum of all jumps of $(hbox{the sum of all jumps of , where L N is the Lebesgue constant. This is an improvement of R. Strichartz (J. Fourier Anal. Appl. 6, 533–536, 2000). |
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