A direct integral decomposition of the wavelet representation (Q2723505)
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scientific article; zbMATH DE number 1614775
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A direct integral decomposition of the wavelet representation |
scientific article; zbMATH DE number 1614775 |
Statements
A direct integral decomposition of the wavelet representation (English)
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5 July 2001
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integral decomposition
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wavelet set
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group representations
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multivariate wavelets
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wavelet representation
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discrete group
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dilation matrix
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Baumslag-Solitar groups
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The authors use the wavelet sets introduced by \textit{X. Dai} and \textit{D. R. Larson} [Mem. Am. Math. Soc. 640 (1998; Zbl 0990.42022)] and a modified technique of \textit{L. Baggett} [Colloq. Math. 60/61, No. 1, 195-203 (1990; Zbl 0743.94009)] to decompose the wavelet representation of the discrete group associated to an arbitrary \(n\times n\) integer dilation matrix as a direct integral of irreducible monomial representations. In particular, they generalize a result of \textit{F. Martin} and \textit{A. Valette} [Experiment. Math. 9, 291-300 (2000)] on the weak equivalence of the regular representation and the wavelet representation of the Baumslag-Solitar groups.
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