, Volume 3, Issue 4, pp 451-456

Wavelet sets in ℝ n

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Abstract

A congruency theorem is proven for an ordered pair of groups of homeomorphisms of a metric space satisfying an abstract dilation-translation relationship. A corollary is the existence of wavelet sets, and hence of single-function wavelets, for arbitrary expansive matrix dilations on L 2 ( n). Moreover, for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the Borel structure of n.

The second author is supported in part by NSF Grant DMS-9401544.
The third author was a Graduate Research Assistant at Workshop in Linear Analysis and Probability, Texas A&M University.