Spectrum is periodic for n-intervals

In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set Ω is periodic, with the period an integral multiple of the measure of Ω. As a consequence we get a structure theorem for such spectral sets and observe that the generic case is that of the equal interval case. © 2010 Elsevier Inc. All rights reserved.