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arXiv · 1108.1882

A note on Sturm-Liouville problems whose spectrum is the set of prime numbers

Angelo B. Mingarelli
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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.

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Angelo B. Mingarelli. 2011-08-09. A note on Sturm-Liouville problems whose spectrum is the set of prime numbers. https://arxiv.org/abs/1108.1882

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