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

 

Rudin varieties in products of two annuli


Author: Sergio E. Zarantonello
Journal: Proc. Amer. Math. Soc. 50 (1975), 174-178
MSC: Primary 32C25
MathSciNet review: 0379885
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Abstract: Let $ Q$ be an annulus and $ \partial Q$ its boundary. If $ f$ is holomorphic in $ Q \times Q$ and its zero set is bounded away from $ \partial Q \times \partial Q$, then there exists a bounded holomorphic function $ F$ with the same zeros as $ f$ such that $ {F^{ - 1}}$ is bounded near $ \partial Q \times \partial Q$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0379885-9
PII: S 0002-9939(1975)0379885-9
Keywords: Rudin variety, multiplicative Cousin problem, holomorphic, annulus, polyannulus
Article copyright: © Copyright 1975 American Mathematical Society