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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