Essential Spectra of One-Dimensional Dirac Operators

Abstract

The present paper estimates or explicitly calculates the essential spectra of one-dimensional Dirac operators L by introducing two one-parameter pencils of Sturm–Liouville operators τ 1(λ) and τ 2(λ) for \({\lambda \in \mathbb{R}}\), considering spectral problems of τ j (λ) with a new spectral parameter, and examining the sets \({\{\lambda \in \mathbb{R} :\,\,\, 0 \notin \sigma_{\rm e}(\tau_j(\lambda))\}}\) for j = 1, 2. Applications are given to illustrate the scope of applicability.