Convex bodies with a point of curvature do not have Fourier bases
| dc.creator | Iosevich, Alex | |
| dc.creator | Katz, Nets Hawk | |
| dc.creator | Tao, Terence | |
| dc.date | 1999-11-23 | |
| dc.date | 1999-11-30 | |
| dc.date.accessioned | 2026-07-07T05:31:44Z | |
| dc.date.available | 2026-07-07T05:31:44Z | |
| dc.description | We prove that no smooth symmetric convex body $Ω$ with at least one point of non-vanishing Gaussian curvature can admit an orthogonal basis of exponentials. (The non-symmetric case was proven by Kolountzakis). This is further evidence of Fuglede's conjecture, which states that such a basis is possible if and only if $Ω$ can tile $R^d$ by translations. | |
| dc.description | 5 pages, no figures, submitted to Amer. J. Math | |
| dc.identifier | https://arxiv.org/abs/math/9911167 | |
| dc.identifier | http://arxiv.org/abs/math/9911167 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79455 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B10 | |
| dc.title | Convex bodies with a point of curvature do not have Fourier bases | |
| dc.type | text |