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- W4313441734 abstract "We study $ mathcal{H}ol(Gammacuptext{Int}(Gamma)) $, the normed algebra of all holomorphic functions defined on some simply connected neighbourhood of a simple closed curve $Gamma$ in $mathbb{C} $, equipped with the supremum norm on $ Gamma $. We explore the geometry of nowhere vanishing, point separating sub-algebras of $ mathcal{H}ol(Gamma cup text{Int}(Gamma)) $. We characterize the extreme points and the exposed points of the unit balls of the said sub-algebras for $Gamma$ analytic. We also characterize the smoothness of an element in these sub-algebras by using Birkhoff-James orthogonality techniques without any restriction on $Gamma$. 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." @default.
- W4313441734 created "2023-01-06" @default.
- W4313441734 creator A5001084419 @default.
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- W4313441734 date "2020-03-28" @default.
- W4313441734 modified "2023-10-18" @default.
- W4313441734 title "Geometry of nowhere vanishing, point separating sub-algebras of $mathcal{H}ol(Gammacuptext{Int}(Gamma))$ and zeros of Holomorphic functions" @default.
- W4313441734 doi "https://doi.org/10.48550/arxiv.2003.12855" @default.
- W4313441734 hasPublicationYear "2020" @default.
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