Tiling and spectral properties of near-cubic domains

• Autorzy: Mihail N. Kolountzakis , Izabella Łaba
• Języki publikacji: EN

Abstrakty

EN

We prove that if a measurable domain tiles ℝ or ℝ² 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.

Kategorie tematyczne

• 52C20: Tilings in 2 dimensions
• 42A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 160
• Numer: 3
• Strony: 287-299

Daty

wydano

2004

Twórcy

autor

Mihail N. Kolountzakis

• Department of Mathematics, University of Crete, Knossos Ave., 714 09 Iraklio, Greece

autor

Izabella Łaba

• Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada

Identyfikatory

DOI

10.4064/sm160-3-6