Monatshefte für Mathematik

, Volume 139, Issue 3, pp 221–225 | Cite as

An Edge Point Gibbs Phenomenon for Fourier Series in Two Dimensions

  • Gilbert Helmberg


 Let f be a function periodic in its two variables x, y with period 2π and having at the origin an ‘edge point jump discontinuity’ (its graph may be roughly described by a cliff with a smooth but possibly inclined rim). The Fourier series of f exhibits a Gibbs phenomenon as in the one-dimensional case but with an affine horizontal deformation depending on the compass direction of the rim at the origin.

2000 Mathematics Subject Classification: 42B99 
Key words: Gibbs phenomenon, Fourier series, jump discontinuity 


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Copyright information

© Springer-Verlag/Wien 2003

Authors and Affiliations

  • Gilbert Helmberg
    • 1
  1. 1.Universität Innsbruck, AustriaAT

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