A note on Sturm-Liouville problems whose spectrum is the set of prime numbers
Classical Analysis and ODEs
2011-11-01 v2
Abstract
We show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book on Sturm-Liouville theory. We also show that there {\it may} exist such a problem if the parameter dependence is nonlinear.
Keywords
Cite
@article{arxiv.1108.1882,
title = {A note on Sturm-Liouville problems whose spectrum is the set of prime numbers},
author = {Angelo B. Mingarelli},
journal= {arXiv preprint arXiv:1108.1882},
year = {2011}
}
Comments
Preprint, Submitted. This is a slightly modified version of the previous submission