On a class of non-self-adjoint periodic boundary value problems with discrete real spectrum

TL;DR

This paper investigates a class of non-self-adjoint periodic boundary value problems, demonstrating that their resolvent operators belong to Schatten classes, which has implications for spectral theory and operator analysis.

Contribution

The paper establishes Schatten class properties of the resolvent operators for a specific class of non-self-adjoint periodic Sturm-Liouville problems with singularities.

Findings

Resolvent operators are in Schatten classes

Eigenvalues are real despite non-self-adjointness

Spectral properties are characterized for these boundary problems

Abstract

In [arXiv:0801.0172] we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.