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arXiv · 1505.06833

On non-periodic tilings of the real line by a function

Mihail N. Kolountzakis·Nir Lev
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Abstract

It is known that a positive, compactly supported function $f \in L^1(\mathbb R)$ 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.

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Mihail N. Kolountzakis, Nir Lev. 2015-10-25. On non-periodic tilings of the real line by a function. https://doi.org/10.1093/imrn%2Frnv283

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