Wavelets generated by layer potentials.
type: Item
instance of: scholarly article
title: Wavelets generated by layer potentials.
zbMATH Open document ID: 1033.42034
DOI: 10.1016/S1063-5203(03)00003-4
published in: Applied and Computational Harmonic Analysis
publication date: 2003-07-30T00:00:00Z
review text: By means of the limit and jump relations of classical potential theory in \(\mathbb{R}^3\), a wavelet theory on a regular surface (like sphere or ellipsoid) is established. The authors use the kernels of the layer potentials to introduce new wavelets on regular surfaces. The multiresolution analysis (i.e., scaling functions, scale spaces, wavelets, detail spaces) is defined. A pyramid scheme (tree algorithm) for fast computation is given. The performance of this wavelet framework is illustrated by the zoom-in property, the detection of a high frequency perturbation and the data compression. Finally, a fast multiscale representation of the solution of exterior Dirichlet and Neumann boundary value problems is given.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 86-08
zbMATH DE Number: 1957121
zbMATH Keywords: wavelets
zbMATH Keywords: regular surface
zbMATH Keywords: layer potential
zbMATH Keywords: limit and jump relations
zbMATH Keywords: multiresolution analysis
zbMATH Keywords: pyramid scheme
zbMATH Keywords: tree algorithm
zbMATH Keywords: zoom-in property
zbMATH Keywords: data compression
author: Willi Freeden
author: Carsten Mayer
reviewed by: Manfred Tasche
MaRDI profile type: Publication
cites work: Q4356573
cites work: Q3848301
cites work: Über die Gaußsche Methode zur angenäherten Berechnung von Integralen
cites work: A survey on spherical spline approximation
cites work: Spherical wavelet transform and its discretization
cites work: Q4380354
cites work: Q4266498
cites work: Q4132990
cites work: Grenz- und Sprungrelationen für Potentiale mit quadratsummierbarer Flächenbelegung
cites work: Symmetrizable linear transformations
cites work: Q5562952
cites work: Q4093822
cites work: Spherical harmonics
cites work: Q5573327
cites work: Q5629947
cites work: Q5620934
full work available at URL: s1063-5203(03)00003-4
OpenAlex ID: W2030829362
description: scientific article; zbMATH DE number 1957121