Universal holomorphic maps with slow growth II. functional analysis methods
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913510870482944 |
|---|---|
| author | Guo, Bin Xie, Song-Yan |
| author_facet | Guo, Bin Xie, Song-Yan |
| contents | By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}. Next, we establish that, in the space of holomorphic maps from $\mathbb{C}^n$ to any connected Oka manifold $Y$, equipped with the compact-open topology, there exists a {\em dense} subset consisting of common {\em frequently hypercyclic} elements for all nontrivial translation operators. To our knowledge, this is new even for $n=1$ and $Y=\mathbb{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06561 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal holomorphic maps with slow growth II. functional analysis methods Guo, Bin Xie, Song-Yan Complex Variables Functional Analysis By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}. Next, we establish that, in the space of holomorphic maps from $\mathbb{C}^n$ to any connected Oka manifold $Y$, equipped with the compact-open topology, there exists a {\em dense} subset consisting of common {\em frequently hypercyclic} elements for all nontrivial translation operators. To our knowledge, this is new even for $n=1$ and $Y=\mathbb{C}$. |
| title | Universal holomorphic maps with slow growth II. functional analysis methods |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2310.06561 |