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arXiv · 1904.10538

Extra invariance of principal shift invariant spaces and the Zak transform

Davide Barbieri·Eugenio Hernandez·Carolina A. Mosquera
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Abstract

We prove a necessary and sufficient condition for a principal shift invariant space of $L^2(\mathbb{R})$ to be invariant under translations by the subgroup $\frac{1}{N} \mathbb{Z}, N>1$. This condition is given in terms of the Zak transform of the group $\frac{1}{N} \mathbb{Z}.$ This result is extended to principal shift invariant spaces generated by a lattice in a general locally compact abelian (LCA) group.

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Davide Barbieri, Eugenio Hernandez, Carolina A. Mosquera. 2019-04-23. Extra invariance of principal shift invariant spaces and the Zak transform. https://arxiv.org/abs/1904.10538

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