Proceedings of the American Mathematical Society

Author(s): Lek-Heng Lim; Judith A. Packer; Keith F. Taylor
Journal: Proc. Amer. Math. Soc. 129 (2001), 3057-3067.
MSC (2000): Primary 65T60, 47N40, 22D20, 22D30; Secondary 22D45, 47L30, 47C05
Posted: April 16, 2001
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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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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
Email: lekheng@math.cornell.edu

Judith A. Packer
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Email: matjpj@leonis.nus.edu.sg

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