English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study $ \mathcal{H}ol(\Gamma\cup\text{Int}(\Gamma)) $, the normed algebraof all holomorphic functions defined on some simply connected neighbourhood ofa simple closed curve $\Gamma$ in $\mathbb{C} $, equipped with the supremumnorm on $ \Gamma $. We explore the geometry of nowhere vanishing, pointseparating sub-algebras of $ \mathcal{H}ol(\Gamma \cup \text{Int}(\Gamma)) $.We characterize the extreme points and the exposed points of the unit balls ofthe said sub-algebras for $\Gamma$ analytic. We also characterize thesmoothness of an element in these sub-algebras by using Birkhoff-Jamesorthogonality techniques without any restriction on $\Gamma$. As a culminationof our study, we assimilate the geometry of the aforesaid sub-algebras withsome classical concepts of complex analysis and establish a connection betweenBirkhoff-James orthogonality and zeros of holomorphic functions.

Geometry of nowhere vanishing, point separating sub-algebras of $\mathcal{H}ol(\Gamma\cup\text{Int}(\Gamma))$ and zeros of Holomorphic functions