The Bohr radius for operator valued functions on simply connected domain
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| Format: | Preprint |
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2024
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| _version_ | 1866915007679168512 |
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| author | Ahammed, Sabir Ahamed, Molla Basir |
| author_facet | Ahammed, Sabir Ahamed, Molla Basir |
| contents | In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $Ω$ in $\mathbb{C}$. Next, we establish a generalization of refined version of the Bohr inequality and the Bohr-Rogosinski inequality with the help of the sequence $φ=\{φ_n(r) \}^{\infty}_{n=0}$ of non-negative continuous functions in $[0,1)$ such that the series $\sum_{n=0}^{\infty}φ_n(r)$ converges locally uniformly on the interval $[0,1)$. All the results are proved to be sharp. Moreover, We establish the Bohr inequality and the Bohr-Rogosinski inequality for the class of operator-valued $ν$-Bloch functions defined in two different simply connected domains, $Ω$ and $Ω_γ$, in $\mathbb{C}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_04000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Bohr radius for operator valued functions on simply connected domain Ahammed, Sabir Ahamed, Molla Basir Complex Variables 30A10, 30B10, 30C50, 30C55, 30F45, 30H30, 46E40, 47A56, 47A63 In this paper, we first establish an improved Bohr inequality for the class of operator-valued holomorphic functions $f$ on a simply connected domain $Ω$ in $\mathbb{C}$. Next, we establish a generalization of refined version of the Bohr inequality and the Bohr-Rogosinski inequality with the help of the sequence $φ=\{φ_n(r) \}^{\infty}_{n=0}$ of non-negative continuous functions in $[0,1)$ such that the series $\sum_{n=0}^{\infty}φ_n(r)$ converges locally uniformly on the interval $[0,1)$. All the results are proved to be sharp. Moreover, We establish the Bohr inequality and the Bohr-Rogosinski inequality for the class of operator-valued $ν$-Bloch functions defined in two different simply connected domains, $Ω$ and $Ω_γ$, in $\mathbb{C}$. |
| title | The Bohr radius for operator valued functions on simply connected domain |
| topic | Complex Variables 30A10, 30B10, 30C50, 30C55, 30F45, 30H30, 46E40, 47A56, 47A63 |
| url | https://arxiv.org/abs/2411.04000 |