Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.01287 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909564159393792 |
|---|---|
| author | Andruchow, Esteban Corach, Gustavo Recht, Lázaro |
| author_facet | Andruchow, Esteban Corach, Gustavo Recht, Lázaro |
| contents | We study the composition operators $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_af=f\circφ_a$, where $$ φ_a(z)=\frac{a-z}{1-\bar{a}z}, $$ for $|a|<1$. These operators are reflections: $C_a^2=1$. We study their eigenspaces $N(C_a\pm 1)$, their relative position (i.e., the intersections between these spaces and their orthogonal complementes for $a\ne b$ in the unit disk) and the symmetries induced by $C_a$ and these eigenspaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01287 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetries and reflections from composition operators in the disk Andruchow, Esteban Corach, Gustavo Recht, Lázaro Complex Variables Functional Analysis 47A05, 47B15, 47B33 We study the composition operators $C_a$ acting on the Hardy space $H^2$ of the unit disk, given by $C_af=f\circφ_a$, where $$ φ_a(z)=\frac{a-z}{1-\bar{a}z}, $$ for $|a|<1$. These operators are reflections: $C_a^2=1$. We study their eigenspaces $N(C_a\pm 1)$, their relative position (i.e., the intersections between these spaces and their orthogonal complementes for $a\ne b$ in the unit disk) and the symmetries induced by $C_a$ and these eigenspaces. |
| title | Symmetries and reflections from composition operators in the disk |
| topic | Complex Variables Functional Analysis 47A05, 47B15, 47B33 |
| url | https://arxiv.org/abs/2307.01287 |