Module-valued ordinary differential equations and structure of solution spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913109319352320 |
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| author | Liu, Shengda Liu, Yu-Zhe Tao, Keyu |
| author_facet | Liu, Shengda Liu, Yu-Zhe Tao, Keyu |
| contents | We define and study ordinary differential equations (ODEs) for functions valued in a Banach module $V$ over a finite-dimensional $\Bbbk$-algebra $\mathitΛ$ by using the tensor of Banach modules. Furthermore, we show that the solution space of a homogeneous linear ODE as above is shown to be a finitely generated $\mathitΛ$-submodule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Module-valued ordinary differential equations and structure of solution spaces Liu, Shengda Liu, Yu-Zhe Tao, Keyu Functional Analysis Category Theory 16G10, 46H25, 34M15 We define and study ordinary differential equations (ODEs) for functions valued in a Banach module $V$ over a finite-dimensional $\Bbbk$-algebra $\mathitΛ$ by using the tensor of Banach modules. Furthermore, we show that the solution space of a homogeneous linear ODE as above is shown to be a finitely generated $\mathitΛ$-submodule. |
| title | Module-valued ordinary differential equations and structure of solution spaces |
| topic | Functional Analysis Category Theory 16G10, 46H25, 34M15 |
| url | https://arxiv.org/abs/2605.00097 |