Tiling and spectral properties of near-cubic domains
Classical Analysis and ODEs
2016-09-07 v2 Metric Geometry
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.
Cite
@article{arxiv.math/0106012,
title = {Tiling and spectral properties of near-cubic domains},
author = {Mihail N. Kolountzakis and Izabella Laba},
journal= {arXiv preprint arXiv:math/0106012},
year = {2016}
}
Comments
11 pages, 3 figures; added a counterexample in dimensions 3 and higher