On the spectral properties of long-range perturbations of a class of block finite difference operators
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909880970903552 |
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| author | Bourget, Olivier Vargas-Mancipe, Angela |
| author_facet | Bourget, Olivier Vargas-Mancipe, Angela |
| contents | We analyze spectral properties of a family of self-adjoint first-order finite difference operators acting on $\ell^2(\mathbb{Z}; \mathbb{C}^2)$ or $\ell^2(\mathbb{Z}_+; \mathbb{C}^2)$. Applying the conjugate operator method, we prove the existence of limiting absorption principles and the absence of singular continuous spectrum for these operators. Our results cover classes of admissible long-range perturbations that have not been previously addressed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the spectral properties of long-range perturbations of a class of block finite difference operators Bourget, Olivier Vargas-Mancipe, Angela Spectral Theory We analyze spectral properties of a family of self-adjoint first-order finite difference operators acting on $\ell^2(\mathbb{Z}; \mathbb{C}^2)$ or $\ell^2(\mathbb{Z}_+; \mathbb{C}^2)$. Applying the conjugate operator method, we prove the existence of limiting absorption principles and the absence of singular continuous spectrum for these operators. Our results cover classes of admissible long-range perturbations that have not been previously addressed. |
| title | On the spectral properties of long-range perturbations of a class of block finite difference operators |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2511.00332 |