On non-Periodic Tilings of the Real Line by a Function

Mihail N. Kolountzakis, Nir Lev

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

It is known that a positive, compactly supported function f ∈ L1(ℝ) can tile by translations only if the translation set is a finite union of periodic sets. We prove that this is not the case if f is allowed to have unbounded support. On the other hand, we also show that if the translation set has finite local complexity, then it must be periodic, even if the support of f is unbounded.

Original languageEnglish
Pages (from-to)4588-4601
Number of pages14
JournalInternational Mathematics Research Notices
Volume2016
Issue number15
DOIs
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© The Author(s) 2015. Published by Oxford University Press. All rights reserved.

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