| Affiliation: | Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201 ; Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 ; Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6 |
| Abstract: | 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  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. |
