Geodesic
Tiling and spectral properties of near-cubic domains
Mihail N. Kolountzakis 1   ; Izabella /Laba 2
1 Department of Mathematics University of Crete Knossos Ave. 714 09 Iraklio, Greece
2 Department of Mathematics University of British Columbia Vancouver, B.C. V6T 1Z2, Canada
Studia Mathematica, Tome 160 (2004) no. 3, pp. 287-299 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm160-3-6
Keywords: prove measurable domain tiles mathbb mathbb translations close enough line segment square respectively admits lattice tiling prove similar result spectral sets dimension example showing there analogue tiling result dimensions higher

Mihail N. Kolountzakis  1   ; Izabella /Laba  2

1 Department of Mathematics University of Crete Knossos Ave. 714 09 Iraklio, Greece
2 Department of Mathematics University of British Columbia Vancouver, B.C. V6T 1Z2, Canada 
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Mihail N. Kolountzakis; Izabella /Laba. Tiling and spectral properties of
 near-cubic domains. Studia Mathematica, Tome 160 (2004) no. 3, pp. 287-299. doi: 10.4064/sm160-3-6

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