Localization operator based on sampling multipliers
type: Item
instance of: scholarly article
title: Localization operator based on sampling multipliers
zbMATH Open document ID: 1112.41018
author: Liwen Qian
published in: Applied and Computational Harmonic Analysis
publication date: 2007-03-08T00:00:00Z
review text: The paper studies the localization operator based on sampling multipliers. The obtained explicit error bounds for approximation in the Paley-Wiener spaces unify several extensions of the Shannon sampling theorem and generalize the localized sampling with special sampling multipliers. By applying the Hermite multiplier in the localized sampling series, exponentially decaying accuracy can be achieved for approximating functions and their derivatives in Paley-Wiener spaces, and practical means for choosing parameters to achieve any desired accuracy for sampling is provided. The localized sampling series significantly improves the convergence rate of sampling expansion in Mayer wavelet subspaces when the Hermite multipliers are used. Numerical experiments are presented to demonstrate the high accuracy performed by using the localized sampling series.
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 5131621
zbMATH Keywords: localization operator
zbMATH Keywords: sampling multiplier
zbMATH Keywords: error estimate
zbMATH Keywords: Hermite function
zbMATH Keywords: Meyer wavelet
MaRDI profile type: Publication
full work available at URL: j.acha.2006.07.001
OpenAlex ID: W1985474173
cites work: Q5680530
cites work: Q4319646
cites work: On the regularized Whittaker-Kotel’nikov-Shannon sampling formula
cites work: Q3338707
cites work: A modification of the Whittaker-Kotelnikov-Shannon sampling series
cites work: Localization of the generalized sampling series and its numerical application
cites work: Q5451847
cites work: A sampling theorem for wavelet subspaces
cites work: Bounds for Truncation Error of the Sampling Expansion
cites work: A direct interpolation method for irregular sampling
cites work: Q4003151
cites work: Uncertainty principles in Hilbert spaces
cites work: Q3267566
cites work: Uniform approximation of functions with discrete approximation functionals
cites work: Q4948769
cites work: Hypercircle inequalities and sampling theory
cites work: Ten Lectures on Wavelets
cites work: Q4423179
cites work: On the smoothness of orthonormal wavelets arising from HDAFs
DOI: 10.1016/J.ACHA.2006.07.001
description: scientific article; zbMATH DE number 5131621