Eigenvalue Bounds for Perturbed Periodic Dirac Operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910652727033856 |
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| author | Jameel, Ghada Shuker Schmidt, Karl Michael |
| author_facet | Jameel, Ghada Shuker Schmidt, Karl Michael |
| contents | 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 in L^1(R)^{2x2} , but only close to the spectral bands as a whole for small V in L^p(R)^{2x2} , p > 1. As auxiliary results, we prove the relative compactness of matrix multiplication operators in L^{2p}(R)^{2x2} 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12467 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenvalue Bounds for Perturbed Periodic Dirac Operators Jameel, Ghada Shuker Schmidt, Karl Michael Spectral Theory 47B28, 34L40, 47A55, 81Q15 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 in L^1(R)^{2x2} , but only close to the spectral bands as a whole for small V in L^p(R)^{2x2} , p > 1. As auxiliary results, we prove the relative compactness of matrix multiplication operators in L^{2p}(R)^{2x2} 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. |
| title | Eigenvalue Bounds for Perturbed Periodic Dirac Operators |
| topic | Spectral Theory 47B28, 34L40, 47A55, 81Q15 |
| url | https://arxiv.org/abs/2410.12467 |