A Direct Integral Decomposition of the Wavelet Representation

Details A Direct Integral Decomposition of the Wavelet Representation A Direct Integral Decomposition of the Wavelet Representation

2000-03-11

arxiv.org/abs/math/0003067v3

Proceedings of the American Mathematical Society, Volume 129, Number 10, October 2001, pp. 3057--3067

Mathematics

Functional Analysis

11 pages

Scientific paper

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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