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Riesz bases of exponentials on unbounded multi-tiles


Authors: Carlos Cabrelli and Diana Carbajal
Journal: Proc. Amer. Math. Soc. 146 (2018), 1991-2004
MSC (2010): Primary 42B99, 42C15; Secondary 42A10, 42A15
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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Additional Information

Carlos Cabrelli
Affiliation: Departamento de Matemática, Universidad de Buenos Aires, Instituto de Matemática “Luis Santaló” (IMAS-CONICET-UBA), Buenos Aires, Argentina
Email: cabrelli@dm.uba.ar

Diana Carbajal
Affiliation: Departamento de Matemática, Universidad de Buenos Aires, Instituto de Matemática “Luis Santaló” (IMAS-CONICET-UBA), Buenos Aires, Argentina
Email: dcarbajal@dm.uba.ar

DOI: https://doi.org/10.1090/proc/13980
Keywords: Riesz bases of exponentials, frames of exponentials, multi-tiling, submulti-tiling, Paley-Wiener spaces, shift-invariant spaces
Received by editor(s): January 24, 2017
Received by editor(s) in revised form: May 8, 2017
Published electronically: January 29, 2018
Additional Notes: The research of the authors was partially supported by Grants: CONICET PIP 11220110101018, PICT-2014-1480, UBACyT 20020130100403BA, UBACyT 20020130100422BA.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2018 American Mathematical Society

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