Tiling and spectral properties of near-cubic domains

Mihail N. Kolountzakis, and Izabella Łaba. "Tiling and spectral properties of near-cubic domains." Studia Mathematica 160.3 (2004): 287-299. <http://eudml.org/doc/284672>.

@article{MihailN2004,
abstract = {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.},
author = {Mihail N. Kolountzakis, Izabella Łaba},
journal = {Studia Mathematica},
keywords = {tiling; lattice tiling; spectral set; near-square domain},
language = {eng},
number = {3},
pages = {287-299},
title = {Tiling and spectral properties of near-cubic domains},
url = {http://eudml.org/doc/284672},
volume = {160},
year = {2004},
}

TY - JOUR
AU - Mihail N. Kolountzakis
AU - Izabella Łaba
TI - Tiling and spectral properties of near-cubic domains
JO - Studia Mathematica
PY - 2004
VL - 160
IS - 3
SP - 287
EP - 299
AB - 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.
LA - eng
KW - tiling; lattice tiling; spectral set; near-square domain
UR - http://eudml.org/doc/284672
ER -