An Algebraic Question Related to the Function Theory for Real Submanifolds of ℠n

  • Gary A. Harris
Part of the Progress in Mathematics book series (PM, volume 4)


The purpose of the following discussion is to advertise a recent result of the author which has application the the problems of local holomorphic approximation and local holomorphic extension for C∞ real submanifolds of ℠n with CR singularity and to pose a geometric question motivated by this result.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Freeman, Tangential Cauchy-Riemann Equations and Uniform Approximation, Pacific J. Math. 33 (1970) 101–108.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer Verlag, New York, 1970.Google Scholar
  3. [3]
    G. Harris, The Traces of Holomorphic Functions on Real Submanifolds of ℂn, Trans. Amer. Math. Soc. (to appear).Google Scholar
  4. [4]
    G. Harris, Higer Order Analogues to the Tangential Cauchy-Riemann Equations for Real Submanifo1ds of ℂn with CR Singularity, Proc. Amer. Math. Soc. (to appear).Google Scholar
  5. [5]
    L. Hormander and J. Wermer, Uniform Approximation on Compact Subsets of ℂn, Math. Scan. 23 (1968), 5–21.MathSciNetGoogle Scholar
  6. [6]
    R. Nirenberg and R. O. Wells, Jr., Approximation Theorems on Differentiable Submanifo1ds of a Complex Manifold, Trans. Amer. Math. Soc. 142 (1969), 15–35.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    G. Tomassini, Trace delle Funzioni 0lomorfe su11a Sottovarieta Ana1iticha Reali d’una Varieta Complessa, Ann. Scuola Norm. Sup. Pisa (1966), 31–43.Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gary A. Harris
    • 1
  1. 1.Department of MathematicsTexas Tech. UniversityTexasUSA

Personalised recommendations