The Gibbs phenomenon for Fourier interpolation
type: Item
instance of: scholarly article
title: The Gibbs phenomenon for Fourier interpolation
zbMATH Open document ID: 0828.42002
author: Gilbert Helmberg
published in: Journal of Approximation Theory
publication date: 1996-01-02T00:00:00Z
review text: For a real-valued function periodic on \(\mathbb{R}\) with period \(2\pi\) and of bounded variation on \([- \pi, \pi]\) the behaviour of the Fourier interpolation polynomial near an isolated jump discontinuity point is investigated. It is revealed the presence of asymmetry in the local Gibbs phenomenon for left and right continuity in case when the jump point coincides with the interpolation node. To obtain information on the local extremum of the Fourier interpolation polynomial \(S^*_n\) derivatives are used and to obtain boundary values of \(S^*_n\) its convexity is investigated. The cases of odd and even number of nodes of a Fourier interpolation polynomial, as well as its asymptotic behaviour, are treated separately.
Mathematics Subject Classification ID: 42A15
zbMATH DE Number: 636056
zbMATH Keywords: Fourier interpolation polynomial
zbMATH Keywords: discontinuity point
zbMATH Keywords: Gibbs phenomenon
reviewed by: M.-B. A. Babaev
MaRDI profile type: Publication
full work available at URL: jath.1994.1059
OpenAlex ID: W1966304853
DOI: 10.1006/JATH.1994.1059
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description: scientific article; zbMATH DE number 636056