Periodicity of the spectrum of a finite union of intervals

Details Periodicity of the spectrum of a finite union of intervals Periodicity of the spectrum of a finite union of intervals

2011-02-27

arxiv.org/abs/1102.5557v1

Mathematics

Classical Analysis and ODEs

4 pages

Scientific paper

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 $e_\lambda(x) = \exp(2\pi i \lambda x)$ form a complete orthonormal system on $L^2(\Omega)$. Such a set $\Lambda$ is called a spectrum of $\Omega$. In this note we present a simplified proof of the fact that any spectrum $\Lambda$ of a set $\Omega$ which is finite union of intervals must be periodic. The original proof is due to Bose and Madan.

Affiliated with

Also associated with

No associations

Rating

Periodicity of the spectrum of a finite union of intervals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Periodicity of the spectrum of a finite union of intervals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodicity of the spectrum of a finite union of intervals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-424270