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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Zero sets and extensions of bounded holomorphic functions in polydiscs

Author: P. S. Chee
Journal: Proc. Amer. Math. Soc. 60 (1976), 109-115
MSC: Primary 32D15
MathSciNet review: 0422678
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Abstract: A sufficient condition for a hypersurface in a polydisc ${U^n}$ to be the zero set of an ${H^\infty }({U^n})$ function is proved. This strengthens a result of Zarantonello and generalizes a result of Rudin. Using this result and a result of Andreotti and Stoll, a partial extension of Alexander’s theorem on extension of bounded holomorphic functions from a hypersurface of ${U^n}$ to ${U^n}$ is obtained. Finally, a generalization of Cima’s extension theorem for ${H^p}$ functions is given.

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Keywords: Polydiscs, bounded holomorphic functions, Hardy classes, zero sets, extension of bounded holomorphic functions, removable singularities, second Cousin problem
Article copyright: © Copyright 1976 American Mathematical Society