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

 

One-sided cluster-set theory in a polydisc


Authors: C. L. Childress and G. L. Csordas
Journal: Proc. Amer. Math. Soc. 77 (1979), 41-47
MSC: Primary 30D40; Secondary 32A40
MathSciNet review: 539628
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Abstract: In this paper, we develop a technique which reduces the investigation of the boundary behavior of a single function f in $ {H^\infty }({U^n}),n > 1$, to the study of the cluster sets of a sequence of functions in $ {H^\infty }(U)$. We also demonstrate the significance and usefulness of one-sided cluster-set theory.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0539628-6
PII: S 0002-9939(1979)0539628-6
Keywords: One-sided cluster sets, angular and principal cluster sets, the Iversen-Doob Theorem, the Lindelöf Theorem, the Gross Cluster-Value Theorem, the Gehring-Lohwater Theorem
Article copyright: © Copyright 1979 American Mathematical Society