A direct integral decomposition of the wavelet representation

Lim, Lek-Heng; Packer, Judith; Taylor, Keith

doi:10.1090/S0002-9939-01-05928-7

A direct integral decomposition of the wavelet representation
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by Lek-Heng Lim, Judith A. Packer and Keith F. Taylor

Proc. Amer. Math. Soc. 129 (2001), 3057-3067

DOI: https://doi.org/10.1090/S0002-9939-01-05928-7

Published electronically: April 16, 2001

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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 $n \times n$ 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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