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.
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This research was partially supported by the NSF of Shandong Province (Grants ZR2012AM002 and ZR2009AQ010).
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Qi, J., Chen, S. Essential Spectra of One-Dimensional Dirac Operators. Integr. Equ. Oper. Theory 74, 7–24 (2012). https://doi.org/10.1007/s00020-012-1988-2
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DOI: https://doi.org/10.1007/s00020-012-1988-2