Periodicity of the spectrum of a finite union of intervals

Mihail N. Kolountzakis

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arXiv · 1102.5557

Periodicity of the spectrum of a finite union of intervals

Mihail N. Kolountzakis

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Abstract

A set $Ω$, of Lebesgue measure 1, in the real line is called spectral if there is a set $Λ$ of real numbers such that the exponential functions $e_λ(x) = \exp(2πi λx)$ form a complete orthonormal system on $L^2(Ω)$. Such a set $Λ$ is called a spectrum of $Ω$. In this note we present a simplified proof of the fact that any spectrum $Λ$ of a set $Ω$ which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.

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BibTeX RIS

Mihail N. Kolountzakis. 2011-02-27. Periodicity of the spectrum of a finite union of intervals. https://arxiv.org/abs/1102.5557

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