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 |
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Pages (from-to) | 4588-4601 |
Number of pages | 14 |
Journal | International Mathematics Research Notices |
Volume | 2016 |
Issue number | 15 |
DOIs | |
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 |
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European Social Fund and Greek national resources | |
Israel Science Foundation | 225/13 |