Riesz bases of exponentials on unbounded multi-tiles

Cabrelli, Carlos; Carbajal, Diana

doi:10.1090/proc/13980

Riesz bases of exponentials on unbounded multi-tiles
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by Carlos Cabrelli and Diana Carbajal

Proc. Amer. Math. Soc. 146 (2018), 1991-2004

DOI: https://doi.org/10.1090/proc/13980

Published electronically: January 29, 2018

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Abstract:

We prove the existence of Riesz bases of exponentials of $L^2(\Omega )$, provided that $\Omega \subset \mathbb {R}^d$ is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property that we call admissibility. This property is satisfied for any bounded domain, so our results extend the known case of bounded multi-tiles. We also extend known results for submulti-tiles and frames of exponentials to the unbounded case.

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