Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910357039087616 |
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| author | Fricain, Emmanuel Lebreton, Romain |
| author_facet | Fricain, Emmanuel Lebreton, Romain |
| contents | In this paper, we study the cyclic vectors of the shift operator $S_b$ acting on de Branges-Rovnyak space $\mathcal H(b)$ associated to a non-extreme point of the closed unit ball of $H^\infty$. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces Fricain, Emmanuel Lebreton, Romain Complex Variables Functional Analysis In this paper, we study the cyclic vectors of the shift operator $S_b$ acting on de Branges-Rovnyak space $\mathcal H(b)$ associated to a non-extreme point of the closed unit ball of $H^\infty$. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity. |
| title | Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2403.04335 |