Hypercyclic subspaces for sequences of finite order differential operators
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866929677730316288 |
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| author | Bernal-González, L. Calderón-Moreno, M. C. López-Salazar, J. Prado-Bassas, J. A. |
| author_facet | Bernal-González, L. Calderón-Moreno, M. C. López-Salazar, J. Prado-Bassas, J. A. |
| contents | It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense $\mathfrak{c}$-dimensional subspace of entire functions, all of whose nonzero members are hypercyclic for the corresponding sequence $(P_n(D))$ of differential operators. In both cases, the subspace can be chosen so as to contain any prescribed hypercylic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypercyclic subspaces for sequences of finite order differential operators Bernal-González, L. Calderón-Moreno, M. C. López-Salazar, J. Prado-Bassas, J. A. Complex Variables Functional Analysis 15A03, 30K15, 46B87, 47A16, 47B91 It is proved that, if $(P_n)$ is a sequence of polynomials with complex coefficients having unbounded valences and tending to infinity at sufficiently many points, then there is an infinite dimensional closed subspace of entire functions, as well a dense $\mathfrak{c}$-dimensional subspace of entire functions, all of whose nonzero members are hypercyclic for the corresponding sequence $(P_n(D))$ of differential operators. In both cases, the subspace can be chosen so as to contain any prescribed hypercylic function. |
| title | Hypercyclic subspaces for sequences of finite order differential operators |
| topic | Complex Variables Functional Analysis 15A03, 30K15, 46B87, 47A16, 47B91 |
| url | https://arxiv.org/abs/2408.00721 |