Browsing by Author "Dai, Xingde."

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    Wavelet sets in ℝ n
    (Council for innovative research, 2015-06-18) Dai, Xingde.; Larson, David R.; Speegle, Darrin m.
    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 (ℝ n). Moreover, for any expansive matrix dilation, it is proven that there are sufficiently many wavelet sets to generate the Borel structure ofℝ n.