Tiles with no spectra
| dc.creator | Kolountzakis, Mihail N. | |
| dc.creator | Matolcsi, Mate | |
| dc.date | 2004-06-07 | |
| dc.date.accessioned | 2026-07-07T05:08:58Z | |
| dc.date.available | 2026-07-07T05:08:58Z | |
| dc.description | We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their $L^2$ space consisting of group characters). This disproves the Universal Spectrum Conjecture of Lagarias and Wang. Further, we construct a set in some finite Abelian group, which tiles the group but has no spectrum. We extend this last example to the groups $\ZZ^d$ and $\RR^d$ (for $d \ge 5$) thus disproving one direction of the Spectral Set Conjecture of Fuglede. The other direction was recently disproved by Tao. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406127 | |
| dc.identifier | http://arxiv.org/abs/math/0406127 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71468 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | 52C22; 20K01; 42B99 | |
| dc.title | Tiles with no spectra | |
| dc.type | text |