Dynamics of the translation semigroup on directed metric trees
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911624739160064 |
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| author | Mangino, Elisabetta Vargas-Moreno, Alvaro |
| author_facet | Mangino, Elisabetta Vargas-Moreno, Alvaro |
| contents | The dynamics of the left translation semigroup $\{T_t\}_{t \geq 0}$ on weighted $L^p$ spaces over a directed metric tree $L(G)$ is investigated. Necessary and sufficient conditions on the weight family $ρ$ for the strong continuity of the semigroup are provided. Furthermore, hypercyclicity and weak mixing properties are characterized in terms of the asymptotic decay of $ρ$ along the tree structure. These results generalize classical $L^p$ translation semigroup dynamics to a graph setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamics of the translation semigroup on directed metric trees Mangino, Elisabetta Vargas-Moreno, Alvaro Functional Analysis Dynamical Systems 47A16, 47D06, 05C20 The dynamics of the left translation semigroup $\{T_t\}_{t \geq 0}$ on weighted $L^p$ spaces over a directed metric tree $L(G)$ is investigated. Necessary and sufficient conditions on the weight family $ρ$ for the strong continuity of the semigroup are provided. Furthermore, hypercyclicity and weak mixing properties are characterized in terms of the asymptotic decay of $ρ$ along the tree structure. These results generalize classical $L^p$ translation semigroup dynamics to a graph setting. |
| title | Dynamics of the translation semigroup on directed metric trees |
| topic | Functional Analysis Dynamical Systems 47A16, 47D06, 05C20 |
| url | https://arxiv.org/abs/2601.07561 |