Local error estimation for sampling problems
type: Item
instance of: scholarly article
title: Local error estimation for sampling problems
zbMATH Open document ID: 1069.65153
published in: Applied Mathematics and Computation
publication date: 2005-01-17T00:00:00Z
review text: This paper is motivated by recent work of \textit{N. Atreas, J. J. Benedetto} and \textit{C. Karanikas} [Sampl. Theory Signal Image Process. 2, No. 1, 1--24 (2003; Zbl 1049.42018)] on local sampling for regular wavelet and Gabor expansions. Their result is complicated in form and the method is difficult to generalize to higher dimensional cases. In this paper, a new method to evaluate the decay of the sampling function is given, so it can be used to derive a more subtle local error estimation for the reconstruction formulas in a multiresolution analysis and shift-invariant space.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 2128781
zbMATH Keywords: local error estimation
zbMATH Keywords: sampling function
zbMATH Keywords: wavelets sampling
zbMATH Keywords: Gabor expansions
zbMATH Keywords: error estimation
zbMATH Keywords: reconstruction formulas
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: decay estimation
zbMATH Keywords: reproducing kernel Hilbert space
author: Shou-yuan Yang
reviewed by: Chengshu Wang
MaRDI profile type: Publication
full work available at URL: j.amc.2003.09.013
OpenAlex ID: W2048184766
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DOI: 10.1016/J.AMC.2003.09.013
description: scientific article; zbMATH DE number 2128781