A note on Sturm-Liouville problems whose spectrum is the set of prime numbers
classification
🧮 math.CA
keywords
sturm-liouvillenumbersproblemspectrumtherewhoseanswersbook
pith:25VVAQZ5 Add to your LaTeX paper
What is a Pith Number?\usepackage{pith}
\pithnumber{25VVAQZ5}
Prints a linked pith:25VVAQZ5 badge after your title and writes the identifier into PDF metadata. Compiles on arXiv with no extra files. Learn more
read the original 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.