The construction ofr-regular wavelets for arbitrary dilations |
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Authors: | Marcin Bownik |
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Affiliation: | (1) Department of Mathematics, University of Michigan, 525 East University Ave., 48109-1109 Ann Arbor, MI |
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Abstract: | Given a dilation matrix A and a natural number r we construct an associated r-regular multiresolution analysis with r-regular wavelet basis. Here a dilation is an n×n expansive matrix A (all eigenvalues λ of A satisfy |λ|>1) with integer entries. This extends a theorem of Strichartz which assumes the existence of a self-affine tiling associated with the dilation A. We also prove that regular wavelets have vanishing moments. |
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Keywords: | 42C15 |
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