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arXiv · 1710.03176

Frames of exponentials and sub-multitiles in LCA groups

Davide Barbieri·Carlos Cabrelli·Eugenio Hernández·Peter Luthy·Ursula Molter·Carolina Mosquera
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Abstract

In this note we investigate the existence of frames of exponentials for $L^2(\Omega)$ in the setting of LCA groups. Our main result shows that sub-multitiling properties of $\Omega \subset \widehat{G}$ with respect to a uniform lattice $\Gamma$ of $\widehat{G}$ guarantee the existence of a frame of exponentials with frequencies in a finite number of translates of the annihilator of $\Gamma$. We also prove the converse of this result and provide conditions for the existence of these frames. These conditions extend recent results on Riesz bases of exponentials and multitilings to frames.

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Davide Barbieri, Carlos Cabrelli, Eugenio Hernández, Peter Luthy, Ursula Molter, Carolina Mosquera. 2017-10-09. Frames of exponentials and sub-multitiles in LCA groups. https://arxiv.org/abs/1710.03176

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