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- W2965061839 abstract "A bounded measurable set $Omegasubset{mathbb R}^d$ is called a spectral set if it admits some exponential orthonormal basis ${e^{2pi i langlelambda,xrangle}: lambdainLambda}$ for $L^2(Omega)$. In this paper, we show that in dimension one $d=1$, any spectrum $Lambda$ with $0inLambda$ of a spectral set $Omega$ with Lebesgue measure normalized to 1 must be rational. Combining previous results that spectrum must be periodic, the Fuglede's conjecture on ${mathbb R}^1$ is now equivalent to the corresponding conjecture on all cyclic groups ${mathbb Z}_{n}.$" @default.
- W2965061839 created "2019-08-13" @default.
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- W2965061839 date "2019-08-07" @default.
- W2965061839 modified "2023-10-18" @default.
- W2965061839 title "Spectrum is rational in dimension one" @default.
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