Abstract
In the context of a general lattice Γ in Rn and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families. This result generalizes the characterization of Frazier, Garrigós, Wang, and Weis about the wavelet families with Γ = Zn and M = 21. In the second part of the paper, we characterize all the MSF wavelets. Moreover, we give a constructive method for the support of the Fourier transform of an MSF wavelet and apply this method by giving examples with particular attention to the quincunx lattice.
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Calogero, A. A characterization of wavelets on general lattices. J Geom Anal 10, 597–622 (2000). https://doi.org/10.1007/BF02921988
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DOI: https://doi.org/10.1007/BF02921988