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

 

Analytic continuation on complex lines


Authors: Joseph A. Cima and Josip Globevnik
Journal: Proc. Amer. Math. Soc. 85 (1982), 411-413
MSC: Primary 32D15; Secondary 30B40, 32A40
MathSciNet review: 656114
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Abstract: The following extension theorem is proved. Let $ \Omega \subset {\mathbf{C}}$ be an open set containing $ \Delta $, the open unit disc in $ {\mathbf{C}}$, and the point 1. Suppose that $ f$ is holomorphic on $ B$, the open unit ball of $ {{\mathbf{C}}^N}$, let $ x \in \partial B$ and assume that for all $ y \in \partial B$ in a neighborhood of $ x$ the function $ \varsigma \to f(\varsigma y)$, holomorphic on $ \Delta $, continues analytically into $ \Omega $. Then $ f$ continues analytically into a neighborhood of $ x$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0656114-3
PII: S 0002-9939(1982)0656114-3
Article copyright: © Copyright 1982 American Mathematical Society