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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Tiling and spectral properties of near-cubic domains

### Tom 160 / 2004

Studia Mathematica 160 (2004), 287-299 MSC: 52C20, 42A99. DOI: 10.4064/sm160-3-6

#### Streszczenie

We prove that if a measurable domain tiles ${\mathbb R}$ or ${\mathbb R}^2$ 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.

#### Autorzy

• Mihail N. KolountzakisDepartment of Mathematics
University of Crete
Knossos Ave.
714 09 Iraklio, Greece
e-mail