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A direct integral decomposition of the wavelet representation

Authors: Lek-Heng Lim, Judith A. Packer and Keith F. Taylor
Journal: Proc. Amer. Math. Soc. 129 (2001), 3057-3067
MSC (2000): Primary 65T60, 47N40, 22D20, 22D30; Secondary 22D45, 47L30, 47C05
Published electronically: April 16, 2001
MathSciNet review: 1840112
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Abstract | References | Similar Articles | Additional Information


In this paper we use the concept of wavelet sets, as introduced by X. Dai and D. Larson, 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 so doing we generalize a result of F. Martin and A. Valette in which they show that the wavelet representation is weakly equivalent to the regular representation for the Baumslag-Solitar groups.

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Additional Information

Lek-Heng Lim
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
Address at time of publication: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Judith A. Packer
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

Keith F. Taylor
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6

Keywords: Wavelet, wavelet set, group representations
Received by editor(s): November 15, 1999
Received by editor(s) in revised form: February 24, 2000
Published electronically: April 16, 2001
Additional Notes: The third author was supported in part by a grant from NSERC Canada.
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society