Global structure of the spectrum of periodic Non-hermitian Jacobi operators

TL;DR

This paper analyzes the spectrum of periodic non-Hermitian Jacobi operators, revealing its global structure through the discriminant and stationary points, and providing conditions for real and single-interval spectra.

Contribution

It introduces a detailed description of the spectrum's global structure and establishes criteria for real and single-interval spectra in non-Hermitian Jacobi operators.

Findings

Spectrum's structure characterized by discriminant and stationary points

Necessary and sufficient conditions for real spectrum

Criteria for spectrum being a single interval

Abstract

The global structure of the spectrum of periodic non-Hermitian Jacobi operators is described by the discriminant and its stationary points. We also give necessary and sufficient conditions for real spectrum and single interval spectrum.