Estimates on the non-real eigenvalues of regular indefinite Sturm-Liouville problems

TL;DR

This paper derives explicit bounds on the real and imaginary parts of non-real eigenvalues in regular indefinite Sturm-Liouville problems, providing insights into their spectral properties.

Contribution

It offers new explicit bounds on non-real eigenvalues for indefinite Sturm-Liouville problems, enhancing understanding of their spectral behavior.

Findings

Explicit bounds on eigenvalues' real parts

Explicit bounds on eigenvalues' imaginary parts

Improved understanding of spectral properties

Abstract

Regular Sturm-Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this note we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the differential expression.