Complex structure that admits complete Nevanlinna-Pick spaces of Hardy type
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914954094837760 |
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| author | Kojin, Kenta |
| author_facet | Kojin, Kenta |
| contents | In this paper, we will characterize those sets, over which every irreducible complete Nevanlinna--Pick space enjoys that its multiplier and supremum norms coincide. Moreover, we will prove that, if there exists an irreducible complete Nevanlinna--Pick space of holomorphic functions on a reduced complex space $X$ whose multiplier algebra is isometrically equal to the algebra of bounded holomorphic functions (we will say that such a space is of $\textbf{Hardy type}$ in this paper), then $X$ must be biholomorphic to the unit disk minus a zero analytic capacity set. This means that the Hardy space is characterized as a unique irreducible complete Nevanlinna--Pick space of Hardy type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex structure that admits complete Nevanlinna-Pick spaces of Hardy type Kojin, Kenta Functional Analysis Complex Variables In this paper, we will characterize those sets, over which every irreducible complete Nevanlinna--Pick space enjoys that its multiplier and supremum norms coincide. Moreover, we will prove that, if there exists an irreducible complete Nevanlinna--Pick space of holomorphic functions on a reduced complex space $X$ whose multiplier algebra is isometrically equal to the algebra of bounded holomorphic functions (we will say that such a space is of $\textbf{Hardy type}$ in this paper), then $X$ must be biholomorphic to the unit disk minus a zero analytic capacity set. This means that the Hardy space is characterized as a unique irreducible complete Nevanlinna--Pick space of Hardy type. |
| title | Complex structure that admits complete Nevanlinna-Pick spaces of Hardy type |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2403.02521 |