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Proceedings of the American Mathematical Society

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Crystallographic multiwavelets in $L^2(\mathbb {R}^d)$


Authors: Ursula Molter and Alejandro Quintero
Journal: Proc. Amer. Math. Soc. 149 (2021), 2445-2460
MSC (2020): Primary 42C40; Secondary 52C22, 20H15
DOI: https://doi.org/10.1090/proc/13998
Published electronically: March 29, 2021
MathSciNet review: 4246796
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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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Additional Information

Ursula Molter
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon I, 1428 Capital Federal, Argentina and IMAS, CONICET/UBA, Argentina
MR Author ID: 126270
Email: umolter@dm.uba.ar

Alejandro Quintero
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina
Email: aquinter@mdp.edu.ar

Keywords: Crystal groups, wavelets, multiresolution analysis, refinement equations.
Received by editor(s): October 26, 2016
Published electronically: March 29, 2021
Additional Notes: This research was partially supported by UBACyT 20020130100403BA and ANPCyT PICT2014-1480
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2021 American Mathematical Society