A boundary uniqueness theorem for holomorphic functions of several complex variables

  • S. I. Pinehuk


If D ⊂ Cn is a region with a smooth boundary and M ⊂ ∂D is a smooth manifold such that for some point p ∈ M the complex linear hull of the tangent plane Tp(M) coincides with Cn, then for each functionf ε A(D) the conditionf¦M=0 implies thatf=0 in D.


Manifold Hull Holomorphic Function Complex Variable Smooth Boundary 
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Literature cited

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    M. Erve, Functions of Several Complex Variables [Russian translation], Moscow (1965).Google Scholar
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    A. Newlander and L. Nirenberg, “Complex analytic coordinates in almost complex manifolds,” Ann. of Math.,65, No. 2, 391–404 (1957).Google Scholar
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    E. Bishop, “Differentiable manifolds in complex euclidean space,” Duke Math. J.,32, No. 1, 1–21 (1965).Google Scholar
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    S. L. Sobolev, “On a theorem in functional analysis,” Matem. Sb.,4(46), No. 3, 471–496 (1938).Google Scholar
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    L. Carleson, “On convergence and growth of partial sums of Fourier series,” Acta Math., 116, Nos. 1–2, 135–157 (1966).Google Scholar
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    R. O. Wells, “On the local holomorphic hull of a submanifold in several complex variables,” Comm. Pure Appl. Math.,19, No. 2, 145–165 (1966).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • S. I. Pinehuk
    • 1
  1. 1.Moscow State UniversityUSSR

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