An Edge Point Gibbs Phenomenon for Fourier Series in Two Dimensions
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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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