Manifolds of continuous BV-functions and vector measure regularity of Banach-Lie groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912299702288384 |
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| author | Glockner, Helge Schmeding, Alexander Suri, Ali |
| author_facet | Glockner, Helge Schmeding, Alexander Suri, Ali |
| contents | We construct a smooth Banach manifold BV$([a,b], M)$ whose elements are suitably-defined functions $f:[a,b] \rightarrow M$ of bounded variation with values in a smooth Banach manifold $M$ which admits a local addition. If the target manifold is a Banach-Lie group $G$, with Lie algebra $\mathfrak{g}$, we obtain a Banach-Lie group BV$([a,b], G)$ with Lie algebra BV$([a, b], \mathfrak{g})$. Strengthening known regularity properties of Banach-Lie groups, we construct a smooth evolution map from a Banach space of $\mathfrak{g}$-valued vector measures on $[0,1]$ to BV$([0,1],G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Manifolds of continuous BV-functions and vector measure regularity of Banach-Lie groups Glockner, Helge Schmeding, Alexander Suri, Ali Functional Analysis 58D15 (primary), 22E65, 22E67, 34A06, 34A12, 45G10, 46E40, 46G10, 46T10 We construct a smooth Banach manifold BV$([a,b], M)$ whose elements are suitably-defined functions $f:[a,b] \rightarrow M$ of bounded variation with values in a smooth Banach manifold $M$ which admits a local addition. If the target manifold is a Banach-Lie group $G$, with Lie algebra $\mathfrak{g}$, we obtain a Banach-Lie group BV$([a,b], G)$ with Lie algebra BV$([a, b], \mathfrak{g})$. Strengthening known regularity properties of Banach-Lie groups, we construct a smooth evolution map from a Banach space of $\mathfrak{g}$-valued vector measures on $[0,1]$ to BV$([0,1],G)$. |
| title | Manifolds of continuous BV-functions and vector measure regularity of Banach-Lie groups |
| topic | Functional Analysis 58D15 (primary), 22E65, 22E67, 34A06, 34A12, 45G10, 46E40, 46G10, 46T10 |
| url | https://arxiv.org/abs/2407.05190 |