Jameel, Ghada Shuker and Schmidt, Karl Michael  ORCID: https://orcid.org/0000-0002-0227-3024
2025.
Eigenvalue bounds for perturbed periodic Dirac operators.
Journal of Spectral Theory
10.4171/jst/556
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Abstract
We characterise regions in the complex plane that contain all non-embedded eigenvalues of a perturbed periodic Dirac operator on the real line with real-valued periodic potential and a generally non-symmetric matrix-valued perturbation V. We show that the eigenvalues are located close to the end-points of the spectral bands for small V∈L 1 (R) 2×2 , but only close to the spectral bands as a whole for small V∈L p (R) 2×2 , p>1. As auxiliary results, we prove the relative compactness of matrix multiplication operators in L 2p (R) 2×2 with respect to the periodic operator under minimal hypotheses, and find the asymptotic solution of the Dirac equation on a finite interval for spectral parameters with large imaginary part.
| Item Type: | Article |
|---|---|
| Date Type: | Published Online |
| Status: | In Press |
| Schools: | Schools > Mathematics |
| Publisher: | EMS Press |
| ISSN: | 1664-039X |
| Date of First Compliant Deposit: | 11 February 2025 |
| Date of Acceptance: | 10 February 2025 |
| Last Modified: | 28 May 2025 10:45 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/176097 |
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