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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Bohr and Besicovitch almost periodic discrete sets and quasicrystals
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by S. Favorov PDF
Proc. Amer. Math. Soc. 140 (2012), 1761-1767 Request permission

Abstract:

A discrete set $A$ in the Euclidean space is almost periodic if the measure with the unit masses at points of the set is almost periodic in the weak sense. We investigate properties of such sets in the case when $A-A$ is discrete. In particular, if $A$ is a Bohr almost periodic set, we prove that $A$ is a union of a finite number of translates of a certain full–rank lattice. If $A$ is a Besicovitch almost periodic set, then there exists a full–rank lattice such that in most cases a nonempty intersection of its translate with $A$ is large.
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Additional Information
  • S. Favorov
  • Affiliation: Mathematical School, Kharkov National University, Swobody sq. 4, Kharkov, 61077 Ukraine
  • MR Author ID: 189658
  • ORCID: 0000-0002-4687-776X
  • Email: sfavorov@gmail.com
  • Received by editor(s): November 11, 2010
  • Received by editor(s) in revised form: January 11, 2011
  • Published electronically: August 22, 2011
  • Communicated by: Mario Bonk
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1761-1767
  • MSC (2010): Primary 52C23; Secondary 42A75, 52C07
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11046-3
  • MathSciNet review: 2869161