Exact local distribution of the absolutely continuous spectral measure
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914867764527104 |
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| author | Li, Xianzhe You, Jiangong Zhou, Qi |
| author_facet | Li, Xianzhe You, Jiangong Zhou, Qi |
| contents | It is well-established that the spectral measure for one-frequency Schrödinger operators with Diophantine frequencies exhibits optimal $1/2$-Hölder continuity within the absolutely continuous spectrum. This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified Hölder continuity of the spectral measure at subcritical energies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact local distribution of the absolutely continuous spectral measure Li, Xianzhe You, Jiangong Zhou, Qi Mathematical Physics Dynamical Systems Spectral Theory It is well-established that the spectral measure for one-frequency Schrödinger operators with Diophantine frequencies exhibits optimal $1/2$-Hölder continuity within the absolutely continuous spectrum. This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified Hölder continuity of the spectral measure at subcritical energies. |
| title | Exact local distribution of the absolutely continuous spectral measure |
| topic | Mathematical Physics Dynamical Systems Spectral Theory |
| url | https://arxiv.org/abs/2407.09278 |