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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Real-analytic submanifolds which are local uniqueness sets for holomorphic functions of $ {\bf C}\sp{3}$


Author: Gary A. Harris
Journal: Trans. Amer. Math. Soc. 277 (1983), 343-351
MSC: Primary 32C05; Secondary 32A10, 32C25
MathSciNet review: 690056
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Abstract: The following problem is considered. Given a real-analytic two-dimensional submanifold, $ M$, of complex Euclidean three-space, are ambient holomorphic functions determined by their values on $ M?$ For a large class of submanifolds a necessary and sufficient condition is found for $ M$ to be a local uniqueness set for holomorphic functions on complex three-space. Finally, the general problem is shown to be related to two-dimensional Nevanlinna theory.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0690056-8
PII: S 0002-9947(1983)0690056-8
Article copyright: © Copyright 1983 American Mathematical Society