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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Riesz bases of exponentials on unbounded multi-tiles
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by Carlos Cabrelli and Diana Carbajal PDF
Proc. Amer. Math. Soc. 146 (2018), 1991-2004 Request permission

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
  • MR Author ID: 308374
  • ORCID: 0000-0002-6473-2636
  • 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
  • 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
  • © Copyright 2018 American Mathematical Society
  • 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
  • MathSciNet review: 3767351