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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    M. Erve, Functions of Several Complex Variables [Russian translation], Moscow (1965).Google Scholar
  2. 2.
    A. Newlander and L. Nirenberg, “Complex analytic coordinates in almost complex manifolds,” Ann. of Math.,65, No. 2, 391–404 (1957).Google Scholar
  3. 3.
    E. Bishop, “Differentiable manifolds in complex euclidean space,” Duke Math. J.,32, No. 1, 1–21 (1965).Google Scholar
  4. 4.
    S. L. Sobolev, “On a theorem in functional analysis,” Matem. Sb.,4(46), No. 3, 471–496 (1938).Google Scholar
  5. 5.
    L. Carleson, “On convergence and growth of partial sums of Fourier series,” Acta Math., 116, Nos. 1–2, 135–157 (1966).Google Scholar
  6. 6.
    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

Personalised recommendations