How large are the spectral gaps?
| dc.creator | Iosevich, Alex | |
| dc.creator | Pedersen, Steen | |
| dc.date | 2001-04-08 | |
| dc.date.accessioned | 2026-07-07T04:41:12Z | |
| dc.date.available | 2026-07-07T04:41:12Z | |
| dc.description | Let $D$ be a bounded domain in ${\Bbb R}^n$ whose boundary has a Minkowski dimension $α<n$. Suppose that $E_Λ= {\{e^{2 πi x \cdot λ}\}}_{λ\in Λ}$, $Λ$ an infinite discrete subset of ${\Bbb R}^n$, is a frame of exponentials for $L^2(D)$, with frame constants $A,B$, $A \leq B$. Then if $$ R \ge C{(\frac{{B|\partial D|}_α}{A|D|} )}^ {\frac{1}{n-α}},$$ where $C$ depends only on the ambient dimension $n$ and ${|\partial D|}_α$ denotes the Minkowski content, then every cube of sidelength $R$ contains at least one element of $Λ$. We give examples that illustrate the extent to which our estimates are sharp. | |
| dc.identifier | https://arxiv.org/abs/math/0104094 | |
| dc.identifier | http://arxiv.org/abs/math/0104094 | |
| dc.identifier | How large are the spectral gaps?, (With S. Pedersen), Pacific J. Math., Volume 192, (2000), pp. 307-314 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61264 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | How large are the spectral gaps? | |
| dc.type | text |