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Tiling and spectral properties of near-cubic domains

Mihail N. Kolountzakis·Izabella Laba
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Abstract

We prove that is a measurable domain tiles R or R^2 by translations, and if it is "close enough" to a line segment or a square respectively, then it admits a lattice tiling. We also prove a similar result for spectral sets in dimension 1, and give an example showing that there is no analogue of the tiling result in dimensions 3 and higher.

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Mihail N. Kolountzakis, Izabella Laba. 2002-06-11. Tiling and spectral properties of near-cubic domains. https://arxiv.org/abs/math/0106012

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