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

Mihail N. Kolountzakis; Nir Lev

doi:10.1093/imrn/rnv283

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

Mihail N. Kolountzakis
, Nir Lev

Department of Mathematics

University of Crete

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	4588-4601
Number of pages	14
Journal	International Mathematics Research Notices
Volume	2016
Issue number	15
DOIs	https://doi.org/10.1093/imrn/rnv283
State	Published - 2016

Bibliographical note

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

Funding

M.K. has been partially supported by the "Aristeia II" action (Project FOURIERDIG) of the operational program Education and Lifelong Learning and is co-funded by the European Social Fund and Greek national resources. N.L. is partially supported by the Israel Science Foundation grant No. 225/13.

Funders	Funder number
European Social Fund and Greek national resources
Israel Science Foundation	225/13

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10.1093/imrn/rnv283

Cite this

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

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