论文标题
$ \ Mathcal {h} ol（γ\ cup \ text {int}（γ））$的几何几何消失的几何形状，分开$ \ mathcal {h}的子代数
Geometry of nowhere vanishing, point separating sub-algebras of $\mathcal{H}ol(Γ\cup\text{Int}(Γ))$ and zeros of Holomorphic functions
论文作者
论文摘要
我们研究$ \ mathcal {h} ol（γ\ cup \ text {int}（γ））$，这是所有holomorphic函数的规范代数，这些函数定义在一些简单连接的封闭曲线$γ$ in $ \ mathbb {c} $中的简单连接的社区，配备了$γ$。我们探索无处消失的几何形状，点分离$ \ Mathcal {h} ol（γ\ cup \ text {int}（γ））$的子代数。我们表征了$γ$分析的上述子代数的极端点和裸露点。我们还通过使用Birkhoff-James正交性技术来表征这些子代数中元素的平滑度，而无需限制$γ$。作为我们研究的高潮，我们用一些经典的复杂分析概念来吸收上述子代数的几何形状，并建立伯克霍夫 - 詹姆斯正交性与霍洛型功能的零之间的联系。
We study $ \mathcal{H}ol(Γ\cup\text{Int}(Γ)) $, the normed algebra of all holomorphic functions defined on some simply connected neighbourhood of a simple closed curve $Γ$ in $\mathbb{C} $, equipped with the supremum norm on $ Γ$. We explore the geometry of nowhere vanishing, point separating sub-algebras of $ \mathcal{H}ol(Γ\cup \text{Int}(Γ)) $. We characterize the extreme points and the exposed points of the unit balls of the said sub-algebras for $Γ$ analytic. We also characterize the smoothness of an element in these sub-algebras by using Birkhoff-James orthogonality techniques without any restriction on $Γ$. As a culmination of our study, we assimilate the geometry of the aforesaid sub-algebras with some classical concepts of complex analysis and establish a connection between Birkhoff-James orthogonality and zeros of holomorphic functions.
