Crystallographic multiwavelets in 𝐿²(ℝ^{𝕕})

Molter, Ursula; Quintero, Alejandro

doi:10.1090/proc/13998

Crystallographic multiwavelets in $L^2(\mathbb {R}^d)$
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by Ursula Molter and Alejandro Quintero

Proc. Amer. Math. Soc. 149 (2021), 2445-2460

DOI: https://doi.org/10.1090/proc/13998

Published electronically: March 29, 2021

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Abstract:

We characterize the scaling function of a crystal Multiresolution Analysis in terms of the vector-scaling function for a Multiresolution Analysis associated to a lattice. We give necessary and sufficient conditions in terms of the symbol matrix in order that an associated crystal wavelet basis exists.

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