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

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

2011-08-09

arxiv.org/abs/1108.1882v2

Electronic J. Differential Equations, Vol. 2011 (2011), No. 123, 1-4

Mathematics

Classical Analysis and ODEs

Preprint, Submitted. This is a slightly modified version of the previous submission

Scientific paper

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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