Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918453318778880 |
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| author | Moszyński, Marcin Świderski, Grzegorz |
| author_facet | Moszyński, Marcin Świderski, Grzegorz |
| contents | We explore to what extent the relation between the absolute continuous spectrum and non-existence of subordinate generalized eigenvectors, known for scalar Jacobi operators, can be formulated also for block Jacobi operators with $d$-dimensional blocks. The main object here allowing to make some progress in that direction is the new notion of the barrier nonsubordinacy. We prove that the barrier nonsubordinacy implies the absolute continuity for block Jacobi operators. Finally, we extend some well-known $d=1$ conditions guaranteeing the absolute continuity to $d \geq 1$ and we give applications of our results to some concrete classes of block Jacobi matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00204 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices Moszyński, Marcin Świderski, Grzegorz Spectral Theory 47B36 (Primary) We explore to what extent the relation between the absolute continuous spectrum and non-existence of subordinate generalized eigenvectors, known for scalar Jacobi operators, can be formulated also for block Jacobi operators with $d$-dimensional blocks. The main object here allowing to make some progress in that direction is the new notion of the barrier nonsubordinacy. We prove that the barrier nonsubordinacy implies the absolute continuity for block Jacobi operators. Finally, we extend some well-known $d=1$ conditions guaranteeing the absolute continuity to $d \geq 1$ and we give applications of our results to some concrete classes of block Jacobi matrices. |
| title | Barrier nonsubordinacy and absolutely continuous spectrum of block Jacobi matrices |
| topic | Spectral Theory 47B36 (Primary) |
| url | https://arxiv.org/abs/2301.00204 |