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Abstract. We show that a characterization of scaling functions for multiresolution analyses given by Hernández and Weiss and that a characterization of low-pass filters given by Gundy both hold for multivariable multiresolution analyses.

Abstract. We investigate the connection between radix representations for Z n and self-affine tilings of R n . We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficiently large.

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