Linear isometries on the annulus: description and spectral properties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929680542597120 |
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| author | Chalendar, Isabelle Oger, Lucas Partington, Jonathan R. |
| author_facet | Chalendar, Isabelle Oger, Lucas Partington, Jonathan R. |
| contents | We give a complete characterisation of the linear isometries of ${\rm Hol}(Ω)$, where $Ω$ is the half-plane, the complex plane or an annulus centered at 0 and symmetric to the unit circle. Moreover, we introduce new techniques to describe the holomorphic maps on the annulus that preserve the unit circle, and we finish by proving results about the spectra of the linear isometries on the annulus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear isometries on the annulus: description and spectral properties Chalendar, Isabelle Oger, Lucas Partington, Jonathan R. Functional Analysis Complex Variables 47B33, 30H05, 47A10 We give a complete characterisation of the linear isometries of ${\rm Hol}(Ω)$, where $Ω$ is the half-plane, the complex plane or an annulus centered at 0 and symmetric to the unit circle. Moreover, we introduce new techniques to describe the holomorphic maps on the annulus that preserve the unit circle, and we finish by proving results about the spectra of the linear isometries on the annulus. |
| title | Linear isometries on the annulus: description and spectral properties |
| topic | Functional Analysis Complex Variables 47B33, 30H05, 47A10 |
| url | https://arxiv.org/abs/2409.16105 |