Hypercyclic and mixing composition operators on $\mathscr{O}_M(\mathbb{R})$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910560020332544 |
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| author | Kalmes, Thomas Przestacki, Adam |
| author_facet | Kalmes, Thomas Przestacki, Adam |
| contents | In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's functional equation and we give a sufficient condition for sequential hypercyclicity of composition operators on $\mathscr{O}_M(\mathbb{R})$. This is used to prove that many mixing composition operators are hypercyclic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_09104 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hypercyclic and mixing composition operators on $\mathscr{O}_M(\mathbb{R})$ Kalmes, Thomas Przestacki, Adam Functional Analysis 47B33, 47A16, 46E10 In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's functional equation and we give a sufficient condition for sequential hypercyclicity of composition operators on $\mathscr{O}_M(\mathbb{R})$. This is used to prove that many mixing composition operators are hypercyclic. |
| title | Hypercyclic and mixing composition operators on $\mathscr{O}_M(\mathbb{R})$ |
| topic | Functional Analysis 47B33, 47A16, 46E10 |
| url | https://arxiv.org/abs/2310.09104 |