Wavelet sets in ℝ n
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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.
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- Wavelet sets in ℝ n
Journal of Fourier Analysis and Applications
Volume 3, Issue 4 , pp 451-456
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