An Abstract Interpretation of the Wavelet Dimension Function Using Group Representations

Methods from abstract harmonic analysis are used to derive a new formulation of the wavelet dimension function and its natural generalizations to higher dimensions. By means of this abstract description, necessary and sufficient conditions are derived for a multiwavelet in N dimensions, relative to...

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Bibliographic Details
Published in:Journal of functional analysis 2000-05, Vol.173 (1), p.1-20
Main Author: Baggett, Lawrence W.
Format: Article
Language:English
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Summary:Methods from abstract harmonic analysis are used to derive a new formulation of the wavelet dimension function and its natural generalizations to higher dimensions. By means of this abstract description, necessary and sufficient conditions are derived for a multiwavelet in N dimensions, relative to an arbitrary expansive integral matrix A, to be a multiwavelet that arises from a multiresolution analysis (MRA), i.e., is an MRA wavelet. Even in the classical case, it is shown that this abstract approach gives new results.
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.1999.3551