Models of holomorphic functions on the symmetrized skew bidisc
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911551878856704 |
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| author | Evans, Connor Lykova, Zinaida A. Young, N. J. |
| author_facet | Evans, Connor Lykova, Zinaida A. Young, N. J. |
| contents | The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( λ_{1}+rλ_{2} ,rλ_{1}λ_{2}): λ_{1}\in \mathbb{D}, λ_{2}\in\mathbb{D}\Big\}, \] for a fixed $r \in (0,1)$. We show the existence of a realization formula and a model formula for such holomorphic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Models of holomorphic functions on the symmetrized skew bidisc Evans, Connor Lykova, Zinaida A. Young, N. J. Complex Variables Functional Analysis 32A10, 30E05, 47B99, 47N70 The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( λ_{1}+rλ_{2} ,rλ_{1}λ_{2}): λ_{1}\in \mathbb{D}, λ_{2}\in\mathbb{D}\Big\}, \] for a fixed $r \in (0,1)$. We show the existence of a realization formula and a model formula for such holomorphic functions. |
| title | Models of holomorphic functions on the symmetrized skew bidisc |
| topic | Complex Variables Functional Analysis 32A10, 30E05, 47B99, 47N70 |
| url | https://arxiv.org/abs/2512.02670 |