Nonlinear inversion of a band-limited Fourier transform
type: Item
instance of: scholarly article
title: Nonlinear inversion of a band-limited Fourier transform
zbMATH Open document ID: 1202.42052
author: Gregory Beylkin
author: Lucas Monzón
published in: Applied and Computational Harmonic Analysis
publication date: 2009-10-20T00:00:00Z
full work available at URL: BEY-MON-2009net.pdf
review text: For a compactly supported function with singularities, this current paper defines two rational approximations based on values of its Fourier transform in a bounded interval, and several Fourier coefficients respectively (the function is extended to periodic one in the second case). It turns out that both approximations avoid Gibbs phenomenon, the poles of rational representations indicate singularity locations of the function, and the approximation errors away from singularities behave as that of uniform approximations. The same method can be used to discuss the impact of adding white noise to the Fourier data, and to estimate density of eigenvalues of Hermitian operators.
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5618751
zbMATH Keywords: rational approximation
zbMATH Keywords: Fourier transform
zbMATH Keywords: singularity
zbMATH Keywords: poles
reviewed by: Youming Liu
MaRDI profile type: Publication
OpenAlex ID: W2058342765
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DOI: 10.1016/J.ACHA.2009.04.003
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description: scientific article; zbMATH DE number 5618751