Comparison theorems for separable wavelet frames
type: Item
instance of: scholarly article
title: Comparison theorems for separable wavelet frames
zbMATH Open document ID: 1183.42035
author: Shannon Bishop
published in: Journal of Approximation Theory
publication date: 2010-01-08T00:00:00Z
review text: The author studies the relationships between the affine densities of the sets \(U\times V\) and \(S\times T\) (both subsets of \(\subset (0,\infty)\times (-\infty,\infty)\)) and the frame properties of \(\{u^{-1/2}f(\frac xu-v)\}_{u\in U,v\in V}\) and \(\{s^{-1/2}f(\frac xs-t)\}_{s\in U,t\in V}\) and in particular it is shown that the quotient of the densities of the dilation sets \(U\) and \(S\) can be bounded from above and below by terms involving the admissibility constants \(C_f= \int_{-\infty}^\infty |\hat f(w)|^2\frac{dw}{|w|}\), \(C_g\) and frame bounds. A similar proportionality result then follows fro the affine densities of \(U\times V\) and \(S\times T\). These results are extended to wavelet frame sequences as well.
reviewed by: Gustaf Gripenberg
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5655029
zbMATH Keywords: affine group
zbMATH Keywords: comparison theorem
zbMATH Keywords: density
zbMATH Keywords: frames
zbMATH Keywords: wavelets
MaRDI profile type: Publication
full work available at URL: j.jat.2008.11.006
OpenAlex ID: W2041790213
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DOI: 10.1016/J.JAT.2008.11.006
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description: scientific article; zbMATH DE number 5655029