A Direct Integral Decomposition of the Wavelet Representation

2000/03/31 by Lek-Heng Lim, Judith A. Packer, Keith F. Taylor · 1 citation
Mathematics · #math.FA #math.RT #msc:46L99 #msc:47N40 #msc:22D40 #msc:22D45 #msc:47D25 #msc:47C05

paper · pdf

published as Proceedings of the American Mathematical Society, Volume 129, Number 10, October 2001, pp. 3057--3067 · 11 pages

arxiv created 2001/12/13 · arxiv updated 2009/11/30

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 × 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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