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Geometry of sub-algebras of Hol(Γ∪Int(Γ)) and zeros of holomorphic functions

Bose, B and Roy, S and Sain, D (2023) Geometry of sub-algebras of Hol(Γ∪Int(Γ)) and zeros of holomorphic functions. In: Banach Journal of Mathematical Analysis, 17 (2).

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Official URL: https://doi.org/10.1007/s43037-022-00242-1


We study Hol(Γ∪Int(Γ)), the normed algebra of all holomorphic functions defined on some simply connected neighbourhood of a simple closed curve Γ in C, equipped with the supremum norm on Γ. We explore the geometry of nowhere vanishing, point separating sub-algebras of Hol(Γ∪Int(Γ)). We characterize the extreme points and the exposed points of the unit balls of the said sub-algebras. We also characterize the smoothness of an element in these sub-algebras by using Birkhoff–James orthogonality techniques. 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.

Item Type: Journal Article
Publication: Banach Journal of Mathematical Analysis
Publisher: Birkhauser
Additional Information: The copyright for this article belongs to Birkhauser.
Keywords: Birkhoff–James orthogonality; Exposed points; Extreme points; Holomorphic functions; Nowhere vanishing, point separating sub-algebra; Smooth points; Zeros of holomorphic functions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 16 Feb 2023 03:39
Last Modified: 16 Feb 2023 03:39
URI: https://eprints.iisc.ac.in/id/eprint/80282

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