A refined Agler decomposition and geometric applications
Greg Knese
TL;DR
This paper presents a refined Agler decomposition for bounded analytic functions on the bidisk, enabling new proofs of extension theorems and characterizations of holomorphic retracts in the polydisk.
Contribution
It introduces a refined Agler decomposition and applies it to reprove extension results and characterize holomorphic retracts, advancing geometric function theory.
Findings
Refined Agler decomposition for bidisk functions
New proof of holomorphic extension without norm increase
Characterization of holomorphic retracts in polydisk
Abstract
We prove a refined Agler decomposition for bounded analytic functions on the bidisk and show how it can be used to reprove an interesting result of Guo et al. related to extending holomorphic functions without increasing their norm. In addition, we give a new treatment of Heath and Suffridge's characterization of holomorphic retracts on the polydisk.
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