Abstract
The arclengths of the graphs Γ(sN(f)) of the partial sums sN(f) of the Fourier series of a piecewise smooth function f with a jump discontinuity grow at the rate O(logN). This problem does not arise if f is continuous, and can be removed by using the standard summability methods.
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Communicated by J.J. Benedetto
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Strichartz, R.S. Gibbs' phenomenon and arclength. The Journal of Fourier Analysis and Applications 6, 533–536 (2000). https://doi.org/10.1007/BF02511544
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DOI: https://doi.org/10.1007/BF02511544