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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0422678-5
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0422678-5
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

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