Complete Norm Preserving Extensions of Holomorphic Functions

2022/04/18 by Jim Agler, Łukasz Kosiński, Agler, Jim +3 · 2 citations
Mathematics · #36A70 #Advanced Banach Space Theory #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2204.08521

openalex publication_date 2022/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for every connected analytic subvariety V there is a pseudoconvex set Ω such that every bounded matrix-valued holomorphic function on V extends isometrically to Ω. We prove that if V is two analytic disks intersecting at one point, if every bounded scalar valued holomorphic function extends isometrically to Ω, then so does every matrix-valued function. In the special case that Ω is the symmetrized bidisk, we show that this cannot be done by finding a linear isometric extension from the functions that vanish at one point.

Cited by

• Function theoretic aspects of the symmetrized polydisc and generalization
• Caratheodory sets in the tridisk

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