The solution of a problem of Coifman, Meyer, and Wickerhauser on wavelet packets
type: Item
instance of: scholarly article
title: The solution of a problem of Coifman, Meyer, and Wickerhauser on wavelet packets
zbMATH Open document ID: 1211.42035
author: Sandra Saliani
published in: Constructive Approximation
publication date: 2011-02-14T00:00:00Z
review text: This paper deals with the question posed by Coifman, Meyer and Wickerhauser of whether a general wavelet packet system can be an orthonormal basis for \(L^2({\mathbb R})\) whenever the ``exceptional set'' associated with the system has Lebesgue zero measure. The author shows that the answer is negative by providing a wavelet packet system for the Lemarié--Meyer wavelet which is not an orthonormal basis and has an exceptional set with Hausdorff dimension 1/2.
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 5851418
zbMATH Keywords: Wavelet packets
zbMATH Keywords: local trace function
zbMATH Keywords: tight frame
zbMATH Keywords: generalized shift-invariant systems
reviewed by: Joan Cerdà
MaRDI profile type: Publication
full work available at URL: s00365-010-9110-y
OpenAlex ID: W2026882657
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DOI: 10.1007/S00365-010-9110-Y
description: scientific article; zbMATH DE number 5851418