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Norm Preserving Extensions of Holomorphic Functions Defined on Varieties in \mathbb Cn

2022/04/18 by Jim Agler, Łukasz Kosiński, Agler, Jim +3
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.2204.08517

Abstract

If V is an analytic set in a pseudoconvex domain Ω, we show there is always a pseudoconvex domain G ⊆ Ω that contains V and has the property that every bounded holomorphic function on V extends to a bounded holomorphic function on G with the same norm. We find such a G for some particular analytic sets. When Ω is an operhedron we show there is a norm on holomorphic functions on V that can always be preserved by extensions to Ω.

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