Gibbs' phenomenon in higher dimensions

DOI10.1016/j.jat.2006.06.006zbMath1129.42016OpenAlexW2014253464MaRDI QIDQ871994

Hans W. Volkmer, Hong Tae Shim, Gilbert G. Walter

Publication date: 27 March 2007

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2006.06.006

zbMATH Keywords

scaling functionwavelet expansionnon-separable wavelet

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) General harmonic expansions, frames (42C15) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Approximation by other special function classes (41A30)

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Cites Work

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• On Gibbs' phenomenon for Riesz spherical means of multiple Fourier integrals and Fourier series
• Gibbs' phenomenon for sampling series and what to do about it
• The Gibbs phenomenon for multiple Fourier integrals
• Localization of a corner-point Gibbs phenomenon for Fourier series in two dimensions
• A corner point Gibbs phenomenon for Fourier series in two dimensions
• On the Gibbs phenomenon for wavelet expansions
• Gibbs phenomenon for wavelets
• Ten Lectures on Wavelets
• Arbitrarily Smooth Orthogonal Nonseparable Wavelets in $\R^2$
• Approximation properties of multivariate wavelets
• Families of Orthogonal Two-Dimensional Wavelets
• Gibbs Phenomenon for Functions of Two Variables
• A construction of \(C^1\)-wavelets on the two-dimensional sphere
• A characterization of dimension functions of wavelets
• Some methods for constructing nonseparable, orthonormal, compactly supported wavelet bases
• Nonseparable, compactly supported interpolating refinable functions with arbitrary smoothness