Wavelet bases adapted to pseudodifferential operators
type: Item
instance of: scholarly article
title: Wavelet bases adapted to pseudodifferential operators
zbMATH Open document ID: 0806.65112
author: Ilona Weinreich
author: Stephan Dahlke
published in: Applied and Computational Harmonic Analysis
publication date: 1995-02-07T00:00:00Z
review text: The paper is concerned with the wavelet Galerkin method for the approximate solution of pseudodifferential equations in \(\mathbb{R}^ 2\). Given a bilinear form \(a(u,v)\) induced by a differential operator or a pseudodifferential operator and given a multiresolution analysis with generator \(\varphi\), the authors construct a wavelet basis \(\{\psi_ e\}\) such that \((a(\varphi(\cdot- k), \psi_ e(\cdot- l))=0\), \(k,l\in \mathbb{Z}^ 2\), \(e\in E\), where \(E\) denotes the set of all vertices of the unit square different from (0,0). The first approach presented in the paper yields compactly supported wavelets under restrictive assumptions on the symbol of the operator. The second approach is based on the concept of biorthogonal wavelets and is more general.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35S15
zbMATH DE Number: 626006
zbMATH Keywords: wavelet Galerkin method
zbMATH Keywords: pseudodifferential equations
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: wavelet basis
zbMATH Keywords: biorthogonal wavelets
reviewed by: Johannes Elschner
MaRDI profile type: Publication
OpenAlex ID: W2060978111
DOI: 10.1006/ACHA.1994.1014
description: scientific article; zbMATH DE number 626006