Opening Gaps in the Spectrum of Strictly Ergodic Jacobi and CMV Matrices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910434787852288 |
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| author | Damanik, David Li, Long |
| author_facet | Damanik, David Li, Long |
| contents | We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labelling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic analytic sampling functions in the subcritical region following from the analyticity of resonance tongue boundaries for both Jacobi and CMV matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Opening Gaps in the Spectrum of Strictly Ergodic Jacobi and CMV Matrices Damanik, David Li, Long Spectral Theory Mathematical Physics Dynamical Systems We prove that dynamically defined Jacobi and CMV matrices associated with generic continuous sampling functions have all gaps predicted by the Gap Labelling Theorem open. We also give a mechanism for generic gap opening for quasi-periodic analytic sampling functions in the subcritical region following from the analyticity of resonance tongue boundaries for both Jacobi and CMV matrices. |
| title | Opening Gaps in the Spectrum of Strictly Ergodic Jacobi and CMV Matrices |
| topic | Spectral Theory Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2404.03864 |