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A set $\Omega$ of Lebesgue measure 1 in the real line is called spectral
if there is a set $\Lambda$ of real numbers such that the exponential
functions $e_\lambda(x) = \exp(2\pi i \lambda x)$, $\lambda\in\Lambda$,
form a complete orthonormal system on $L2(\Omega)$. Such a set $\Lambda$
is called a spectrum of $\Omega$, and the pair $(\Omega,\Lambda)$ is
called a spectral pair.
In this talk I will present a proof that any spectrum
$\Lambda$ of a set $\Omega$ which is finite union of intervals must be
periodic and thus obtain a structure theorem for such spectral pairs.
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