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Transactions of the American Mathematical Society

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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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  • [C-L] E. F. Collingwood and A. T. Lohwater, The theory of cluster sets, Cambridge Univ. Press, London, 1966. MR 0231999 (38:325)
  • [G-R] H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer-Verlag, New York, 1970. MR 0316742 (47:5290)
  • [Gab] A. M. Gabrielov, Formal relations between analytic functions, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 1056-1088. MR 0346184 (49:10910)
  • [H-1] G. A. Harris, The traces of holomorphic functions on real submanifolds, Trans. Amer. Math. Soc. 242 (1978), 205-223. MR 0477120 (57:16664)
  • [H-2] -, Geometry near a C. R. singularity, Illinois J. Math. 25 (1981), 147-158. MR 602905 (83g:32020)
  • [M] P. Milman, Analytic and polynomial homomorphisms of analytic rings, Math. Ann. 232 (1978), 247-253. MR 0492359 (58:11486)

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Article copyright: © Copyright 1983 American Mathematical Society

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