A class of non-convex polytopes that admit no orthonormal basis of exponentials
| dc.creator | Kolountzakis, Mihail N. | |
| dc.creator | Papadimitrakis, Michael | |
| dc.date | 2001-01-26 | |
| dc.date.accessioned | 2026-07-07T04:39:49Z | |
| dc.date.available | 2026-07-07T04:39:49Z | |
| dc.description | A conjecture of Fuglede states that a bounded measurable set D, of measure 1, can tile space by translations if and only if the Hilbert space L^2(D) has an orthonormal basis consisting of exponentials exp(i 2 pi lambda x). If D has the latter property it is called spectral. Let D be a polytope with the following property: there is a direction u such that, of all the polytope faces perpendicular to u, the total area of the faces pointing in the positive u direction is more than the total area of the faces pointing in the negative u direction. It is almost obvious that such a polytope D cannot tile space by translation. We prove in this paper that such a domain is also not spectral, which agrees with Fuglede's conjecture. | |
| dc.identifier | https://arxiv.org/abs/math/0101217 | |
| dc.identifier | http://arxiv.org/abs/math/0101217 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60825 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Metric Geometry | |
| dc.subject | 42 | |
| dc.title | A class of non-convex polytopes that admit no orthonormal basis of exponentials | |
| dc.type | text |