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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.06209 |
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| _version_ | 1866908907465605120 |
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| author | Czornik, Adam Kitzing, Konrad Siegmund, Stefan |
| author_facet | Czornik, Adam Kitzing, Konrad Siegmund, Stefan |
| contents | In this note we introduce a notion of dichotomy which generalizes the classical concept of exponential dichotomy and the recent notion of Bohl dichotomy. A key attribute is the discussion of the sets of subspaces of the state space on which the dichotomy estimates are uniform. Two main results are a dichotomy spectral theorem based on our notion of dichotomy which is uniform on subspaces and a formula for the dichotomy spectral intervals which is new for the Bohl dichotomy spectrum as well as for the classical exponential dichotomy spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dichotomies uniform on subspaces and formulas for dichotomy spectra Czornik, Adam Kitzing, Konrad Siegmund, Stefan Dynamical Systems Functional Analysis 37D25 In this note we introduce a notion of dichotomy which generalizes the classical concept of exponential dichotomy and the recent notion of Bohl dichotomy. A key attribute is the discussion of the sets of subspaces of the state space on which the dichotomy estimates are uniform. Two main results are a dichotomy spectral theorem based on our notion of dichotomy which is uniform on subspaces and a formula for the dichotomy spectral intervals which is new for the Bohl dichotomy spectrum as well as for the classical exponential dichotomy spectrum. |
| title | Dichotomies uniform on subspaces and formulas for dichotomy spectra |
| topic | Dynamical Systems Functional Analysis 37D25 |
| url | https://arxiv.org/abs/2411.06209 |