Schur-Agler class and Carathéodory extremal functions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915971327852544 |
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| author | Biswas, Anindya |
| author_facet | Biswas, Anindya |
| contents | We study the role of Carathéodory extremal functions in the Schur-Agler class generated by a collection of test functions. We show that under certain conditions, $\mathbb{D}$ and $\mathbb{D}^2$ are the only domains where finitely many test functions can generate the Schur class. As applications, we give a description of the Carathéodory extremals in the unit ball of the multiplier algebra of the Drury-Arveson space and give operator-theoretic Herglotz representations for any Carathéodory hyperbolic domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schur-Agler class and Carathéodory extremal functions Biswas, Anindya Complex Variables Primary 47A48, 32F45, Secondary 32E30 We study the role of Carathéodory extremal functions in the Schur-Agler class generated by a collection of test functions. We show that under certain conditions, $\mathbb{D}$ and $\mathbb{D}^2$ are the only domains where finitely many test functions can generate the Schur class. As applications, we give a description of the Carathéodory extremals in the unit ball of the multiplier algebra of the Drury-Arveson space and give operator-theoretic Herglotz representations for any Carathéodory hyperbolic domain. |
| title | Schur-Agler class and Carathéodory extremal functions |
| topic | Complex Variables Primary 47A48, 32F45, Secondary 32E30 |
| url | https://arxiv.org/abs/2510.17658 |