Cowen-Douglas operators and analytic continuation
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911101091840000 |
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| author | Pietrzycki, Paweł |
| author_facet | Pietrzycki, Paweł |
| contents | In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left inverse is a Cowen-Douglas operator. We investigate how the analytic continuations of functions from an invariant subspace of this Cowen-Douglas operator relate to the spectrum of its restriction to that subspace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cowen-Douglas operators and analytic continuation Pietrzycki, Paweł Functional Analysis Complex Variables Differential Geometry Spectral Theory In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left inverse is a Cowen-Douglas operator. We investigate how the analytic continuations of functions from an invariant subspace of this Cowen-Douglas operator relate to the spectrum of its restriction to that subspace. |
| title | Cowen-Douglas operators and analytic continuation |
| topic | Functional Analysis Complex Variables Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2505.05649 |