Irregular wavelet/Gabor frames
type: Item
instance of: scholarly article
title: Irregular wavelet/Gabor frames
zbMATH Open document ID: 1016.42021
DOI: 10.1016/S1063-5203(02)00002-7
published in: Applied and Computational Harmonic Analysis
publication date: 2003-04-02T00:00:00Z
review text: Regular Gabor frames for \(L^2(\mathbb{R})\) have the form \(\{e^{imbx}g(x-na)\}_{m,n\in \mathbb{Z}}\) for suitable parameters \(a,b>0\) and \(g\in L^2(\mathbb{R})\); they are relatively well understood by now. Using perturbation methods, the authors obtain conditions implying that an irregular Gabor system \(\{e^{i \lambda_{m,n}x}g(x-\mu_{m,n})\}_{m,n\in \mathbb{Z}}\) is a frame. In particular, certain decay and regularity conditions on \(g\) leads to the frame property for the irregular system if \(\{e^{imbx}g(x-na)\}_{m,n\in \mathbb{Z}}\) is a frame for some \(a,b>0\) for which \(\sup |\lambda_{m,n}-mb|\) and \(\sup |\mu_{m,n}-na|\) are sufficiently small. Similar results are derived for irregular wavelet frames.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1891391
zbMATH Keywords: Gabor frames
zbMATH Keywords: regularity
zbMATH Keywords: irregular wavelet frames
author: Wenchang Sun
author: Xing-Wei Zhou
MaRDI profile type: Publication
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full work available at URL: s1063-5203(02)00002-7
OpenAlex ID: W2007250092
description: scientific article; zbMATH DE number 1891391