Two new open mapping theorems for analytic multivalued functions

Baribeau, Line; Harbottle, Sarah

doi:10.1090/S0002-9939-1992-1086321-6

Two new open mapping theorems for analytic multivalued functions
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by Line Baribeau and Sarah Harbottle

Proc. Amer. Math. Soc. 115 (1992), 1009-1012

DOI: https://doi.org/10.1090/S0002-9939-1992-1086321-6

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Abstract:

It is conjectured that the image $U$ of a domain $D$, under an analytic multivalued function $K$, satisfies $U \cap \partial U \subset { \cap _{\lambda \in D}}K(\lambda )$ if the values of $K$ are polynomially convex sets. We prove that this conjecture is true in the two special cases when $K$ is convex-valued and polar-valued.

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