Bieberbach conjecture, Bohr radius, Bloch constant and Alexander's theorem in infinite dimensions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917770222895104 |
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| author | Hamada, Hidetaka Kohr, Gabriela Kohr, Mirela |
| author_facet | Hamada, Hidetaka Kohr, Gabriela Kohr, Mirela |
| contents | In this paper, we investigate holomorphic mappings $F$ on the unit ball $\mathbb{B}$ of a complex Banach space of the form $F(x)=f(x)x$, where $f$ is a holomorphic function on $\mathbb{B}$. First, we investigate criteria for univalence, starlikeness and quasi-convexity of type $B$ on $\mathbb{B}$. Next, we investigate a generalized Bieberbach conjecture, a covering theorem and a distortion theorem, the Fekete-Szegö inequality, lower bound for the Bloch constant, and Alexander's type theorem for such mappings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04028 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bieberbach conjecture, Bohr radius, Bloch constant and Alexander's theorem in infinite dimensions Hamada, Hidetaka Kohr, Gabriela Kohr, Mirela Complex Variables In this paper, we investigate holomorphic mappings $F$ on the unit ball $\mathbb{B}$ of a complex Banach space of the form $F(x)=f(x)x$, where $f$ is a holomorphic function on $\mathbb{B}$. First, we investigate criteria for univalence, starlikeness and quasi-convexity of type $B$ on $\mathbb{B}$. Next, we investigate a generalized Bieberbach conjecture, a covering theorem and a distortion theorem, the Fekete-Szegö inequality, lower bound for the Bloch constant, and Alexander's type theorem for such mappings. |
| title | Bieberbach conjecture, Bohr radius, Bloch constant and Alexander's theorem in infinite dimensions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2409.04028 |