On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

TL;DR

This paper proves that a class of PT-symmetric periodic eigenproblems with boundary and interior singularities has a purely real spectrum, extending previous results to a broader class of potentials.

Contribution

It extends the class of potentials for which the spectrum of PT-symmetric periodic problems is proven to be purely real.

Findings

Spectrum of the considered PT-symmetric problem is purely real

Results extend previous findings to a larger class of potentials

Provides mathematical proof for spectral properties of singular eigenproblems

Abstract

We prove that the spectrum of a certain PT-symmetric periodic problem is purely real. Our results extend to a larger class of potentials those recently found by Brian Davies [math.SP/0702122] and John Weir [arXiv:0711.1371].