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   -> Volume 6, Issue 2


Preprint: Composite Wavelet Bases for Operator Equations
 
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"Wolfgang Dahmen" (dahmen@igpm.rwth-aachen.de)
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PostPosted: Tue Jan 28, 1997 1:40 pm    
Subject: Preprint: Composite Wavelet Bases for Operator Equations
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#2 Preprint: Composite Wavelet Bases for Operator Equations

the following paper is available under

http://www.igpm.rwth-aachen.de/~dahmen

or on the ftp server

ftp.igpm.rwth-aachen.de

The papers can be found in the directory of the respective authors
/pub/dahmen/file.ps.Z

Title: Composite Wavelet Bases for Operator Equations

Authors: Wolfgang Dahmen, Reinhold Schneider

Abstract: This paper is concerned with the construction of
biorthogonal wavelet bases defined on a union of parametric images of
the unit $d$-cube. These bases are to satisfy certain requirements
imposed by applications to a class of operator equations acting on
such domains. This covers also elliptic boundary value problems
although this study is primarily motivated by our previous analysis of
wavelet methods for pseudo-differential equations with special
emphasis on boundary integral equations. In this case it is natural
to model the boundary surface as a union of parametric images of the
unit cube. It will be shown how to construct wavelet bases on the
surface which are composed of wavelet bases defined on each surface
patch. Here the relevant properties are the validity of norm
equivalences in certain ranges of Sobolev scales as well as
appropriate moment conditions.
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