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Gibbs-Wilbraham splines

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Abstract

If a function with a jump discontinuity is approximated in the norm ofL 2[−1,1] by a periodic spline of orderk with equidistant knots, a behavior analogous to the Gibbs-Wilbraham phenomenon for Fourier series occurs. A set of cardinal splines which play the role of the sine integral function of the classical phenomenon is introduced. It is then shown that ask becomes large, the phenomenon for splines approaches the classical phenomenon.

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Authors and Affiliations

  1. Department of Mathematics, Weber State University, 84408-1702, Ogden, Utah, USA

    J. Foster & F. B. Richards

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  1. J. Foster
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  2. F. B. Richards
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Communicated by Ronald A. DeVore.

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Foster, J., Richards, F.B. Gibbs-Wilbraham splines. Constr. Approx 11, 37–52 (1995). https://doi.org/10.1007/BF01294337

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  • DOI: https://doi.org/10.1007/BF01294337

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