Spectrum is periodic for n-Intervals

TL;DR

This paper proves that spectral sets composed of finitely many intervals in R have periodic spectra, leading to a structural understanding and highlighting the generic case of equal intervals.

Contribution

It establishes the periodicity of spectra for unions of finitely many intervals and provides a structure theorem for these spectral sets.

Findings

Spectra are periodic with period multiple of the measure of the set

Structural characterization of spectral sets as unions of equal intervals

Generic case corresponds to equal interval unions

Abstract

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 is periodic, with the period an integral multiple of the measure of the set. 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.