Anisotropic curl-free wavelet bases on the unit cube
type: Item
instance of: scholarly article
title: Anisotropic curl-free wavelet bases on the unit cube
zbMATH Open document ID: 1277.42045
publication date: 2013-03-28T00:00:00Z
review text: Curl-free wavelet bases have been investigated on two-dimensional and three-dimensional space. It is important to construct curl-free wavelet bases on bounded domains. Anisotropic divergence-free wavelets on the hypercube have been studied. This paper is to study anisotropic curl-free wavelets on the unit cube. The authors construct anisotropic curl-free wavelets on the unit cube satisfying specific boundary conditions. These wavelets are stable in curl-free space and the wavelet transform has a fast algorithm. The complement space for curl-free space and a Helmholtz decomposition are given for square integrable space on the unit cube. Besides, the expression of curl and div operators in terms of wavelet coordinates, as well as the corresponding norm equivalences, are also studied and provided. This study on anisotropic curl-free wavelets on bounded domains is systematic and in a constructive way.
reviewed by: Yankui Sun
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 6149097
zbMATH Keywords: anisotropic
zbMATH Keywords: curl-free wavelets
zbMATH Keywords: unit cube
zbMATH Keywords: Helmholtz decomposition
author: Ying-chun Jiang
MaRDI profile type: Publication
full work available at URL: s10114-012-1604-z
OpenAlex ID: W2158754910
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DOI: 10.1007/S10114-012-1604-Z
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6149097