Fuglede's conjecture is false in 5 and higher dimensions
| dc.creator | Tao, Terence | |
| dc.date | 2003-06-08 | |
| dc.date | 2003-06-09 | |
| dc.date.accessioned | 2026-07-07T04:58:40Z | |
| dc.date.available | 2026-07-07T04:58:40Z | |
| dc.description | We give an example of a set $Ω\subset \R^5$ which is a finite union of unit cubes, such that $L^2(Ω)$ admits an orthonormal basis of exponentials $\{\frac{1}{|Ω|^{1/2}} e^{2πi ξ_j \cdot x}: ξ_j \in Λ\}$ for some discrete set $Λ\subset \R^5$, but which does not tile $\R^5$ by translations. This answers a conjecture of Fuglede in the negative, at least in 5 and higher dimensions. | |
| dc.description | 8 pages, no figures, 2 matrices; submitted, Math Research Letters | |
| dc.identifier | https://arxiv.org/abs/math/0306134 | |
| dc.identifier | http://arxiv.org/abs/math/0306134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67732 | |
| dc.subject | Combinatorics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 20K01; 42B99 | |
| dc.title | Fuglede's conjecture is false in 5 and higher dimensions | |
| dc.type | text |