Representation of differential operators in wavelet basis
type: Item
instance of: scholarly article
title: Representation of differential operators in wavelet basis
zbMATH Open document ID: 1075.47028
DOI: 10.1016/S0898-1221(04)90083-1
author: M. A. Hajji
author: S. Melkonian
author: Rémi Vaillancourt
publication date: 2005-03-08T00:00:00Z
review text: The paper under review provides a formula for matrix representations of general partial differential operators of the form \(g(\partial_x, \partial_y)\), where \(g\) is an arbitrary analytic function of two variables. The representations are done with respect to two-dimensional periodic orthonormal wavelet bases. In this sense, the paper generalizes the work of \textit{G. Beylkin} [SIAM J. Numer. Anal. 29, No. 6, 1716--1740 (1992; Zbl 0766.65007)].
reviewed by: Wojciech Czaja
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 35R99
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 2142364
zbMATH Keywords: wavelets
zbMATH Keywords: partial differential operators
zbMATH Keywords: circulant
zbMATH Keywords: block circulant
MaRDI profile type: Publication
cites work: Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
cites work: Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)
cites work: Q3784635
cites work: Orthonormal bases of compactly supported wavelets
cites work: Ten Lectures on Wavelets
cites work: Continuous and Discrete Wavelet Transforms
cites work: Q4003151
cites work: Image compression through wavelet transform coding
cites work: Fast Wavelet Based Algorithms for Linear Evolution Equations
cites work: Wavelet Methods for Fast Resolution of Elliptic Problems
cites work: Galerkin-wavelet methods for two-point boundary value problems
cites work: On the Representation of Operators in Bases of Compactly Supported Wavelets
cites work: Fast wavelet transforms and numerical algorithms I
cites work: On the adaptive numerical solution of nonlinear partial differential equations in wavelet bases
cites work: Non-separable bidimensional wavelet bases
cites work: Arbitrarily Smooth Orthogonal Nonseparable Wavelets in $\R^2$
cites work: Q3208805
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142364