Abstract.
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.
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Received February 7, 2002; in revised form May 24, 2002 Published online April 4, 2003
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Helmberg, G. An Edge Point Gibbs Phenomenon for Fourier Series in Two Dimensions. Monatsh. Math. 139, 221–225 (2003). https://doi.org/10.1007/s00605-002-0518-8
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DOI: https://doi.org/10.1007/s00605-002-0518-8