Fuglede's conjecture fails in dimension 4
| dc.creator | Matolcsi, Mate | |
| dc.date | 2006-11-30 | |
| dc.date.accessioned | 2026-07-07T07:33:31Z | |
| dc.date.available | 2026-07-07T07:33:31Z | |
| dc.description | In this note we give an example of a set $\W\subset \R^4$ such that $L^2(\W)$ admits an orthonormal basis of exponentials $\{\frac{1}{|\W |^{1/2}}e^{2πi x, ξ}\}_{ξ\inŁ}$ for some set $Ł\subset\R^4$, but which does not tile $\R^4$ by translations. This improves Tao's recent 5-dimensional example, and shows that one direction of Fuglede's conjecture fails already in dimension 4. Some common properties of translational tiles and spectral sets are also proved. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611936 | |
| dc.identifier | http://arxiv.org/abs/math/0611936 | |
| dc.identifier | Proc. Amer. Math. Soc. 133 (2005), no. 10, 3021--3026 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119485 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.subject | 42B99, 20K01 | |
| dc.title | Fuglede's conjecture fails in dimension 4 | |
| dc.type | text |