Approximate wavelets and the approximation of pseudodifferential operators
type: Item
instance of: scholarly article
title: Approximate wavelets and the approximation of pseudodifferential operators
zbMATH Open document ID: 0932.65149
published in: Applied and Computational Harmonic Analysis
publication date: 1999-10-06T00:00:00Z
review text: In this interesting paper, the authors introduce an approximate multiresolution analysis for spaces generated by smooth functions providing high-order semi-analytic cubature formulas for multidimensional integral operators of mathematical physics. Since these functions satisfy refinement equations with any prescribed accuracy, wavelet-type methods can be applied. An approximate decomposition of the finest scale space into almost orthogonal wavelet spaces is obtained. For the Gaussian function, properties of analytic prewavelets are studied and the projections onto the wavelet spaces are described. The wavelets retain the property of the scaling function to provide efficient analytic expressions of important integral operators, which leads to sparse and semi-analytic representations of these operators.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65R20
zbMATH DE Number: 1310893
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: approximate wavelets
zbMATH Keywords: approximate multiresolution analysis
zbMATH Keywords: almost orthogonal wavelet spaces
zbMATH Keywords: sparse and semi-analytic representations of integral operators
author: V. Maz'ya
author: Gunther Schmidt
reviewed by: Manfred Tasche
MaRDI profile type: Publication
OpenAlex ID: W2017771068
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DOI: 10.1006/ACHA.1998.0253
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description: scientific article; zbMATH DE number 1310893