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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two new open mapping theorems for analytic multivalued functions


Authors: Line Baribeau and Sarah Harbottle
Journal: Proc. Amer. Math. Soc. 115 (1992), 1009-1012
MSC: Primary 32E20; Secondary 30G30, 46J15
MathSciNet review: 1086321
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1086321-6
PII: S 0002-9939(1992)1086321-6
Article copyright: © Copyright 1992 American Mathematical Society