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Gibbs' phenomenon and arclength

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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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Authors and Affiliations

  1. Mathematics Department, Cornell University, Malott Hall, 14853, Ithaca, NY

    Robert S. Strichartz

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  1. Robert S. Strichartz
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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

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