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- W2953036771 abstract "Let $D$ be a bounded domain in ${Bbb R}^n$ whose boundary has a Minkowski dimension $alpha<n$. Suppose that $E_{Lambda}= {{e^{2 pi i x cdot lambda}}}_{lambda in Lambda}$, $Lambda$ 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 $$ R ge C{(frac{{B|partial D|}_{alpha}}{A|D|} )}^ {frac{1}{n-alpha}},$$ where $C$ depends only on the ambient dimension $n$ and ${|partial D|}_{alpha}$ denotes the Minkowski content, then every cube of sidelength $R$ contains at least one element of $Lambda$. We give examples that illustrate the extent to which our estimates are sharp." @default.
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- W2953036771 date "2001-04-08" @default.
- W2953036771 modified "2023-10-12" @default.
- W2953036771 title "How large are the spectral gaps" @default.
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