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Proceedings of the American Mathematical Society

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Bolzano's theorem in several complex variables


Author: Mau Hsiang Shih
Journal: Proc. Amer. Math. Soc. 79 (1980), 32-34
MSC: Primary 32H99
DOI: https://doi.org/10.1090/S0002-9939-1980-0560578-1
MathSciNet review: 560578
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Omega $ be a bounded domain in $ {C^n}$ containing the origin. Let $ f:\bar \Omega \to {C^n}$ be analytic in $ \Omega $ and continuous in $ \bar \Omega $, and $ \operatorname{Re} \bar z \cdot f(z) > 0$ for $ z \in \partial \Omega $. It is shown that f has exactly one zero in $ \Omega $.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0560578-1
Keywords: Analytic functions, Bolzano's theorem, homotopy invariance, subvariety
Article copyright: © Copyright 1980 American Mathematical Society

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