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   -> Volume 7, Issue 9


Preprint: Application of the wavelet multiplicity function
 
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Lawrence Baggett (baggett@euclid.colorado.edu)
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PostPosted: Tue Aug 25, 1998 10:25 pm    
Subject: Preprint: Application of the wavelet multiplicity function
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#2 Preprint: Application of the wavelet multiplicity function

Title:
Application of the wavelet multiplicity function
to MRA wavelets.

Author:
Lawrence W. Baggett

Abstract: Methods from abstract harmonic analysis are used to derive
necessary and sufficient conditions for a multiwavelet in $n$
dimensions, relative to an arbitrary expansive integral matrix, to be
a multiwavelet that arises from a multiresolution analysis, i.e., is
an MRA wavelet. In this paper, we make use of some relatively
abstract functional analytic notions (specifically, multiplicity
theory for projection-valued measures, and Stone's Theorem on unitary
representations of locally compact abelian groups) that have been
shown to be associated to wavelets. We use these abstract notions to
derive some necessary, some sufficient, and some both necessary and
sufficient conditions for a wavelet to be an MRA wavelet.

This can be retrieved from the following URL.

http://amath-www.colorado.edu/math/faculty/baggett
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