Analytic Properties of Holomorphic Functions

  • Carlos A. Berenstein
  • Roger Gay
Part of the Graduate Texts in Mathematics book series (GTM, volume 125)


At the end of Chapter 1 we introduced the holomorphic functions, that is, those functions fC1(Ω) that satisfy the Cauchy-Riemann differential equation \(\frac{{\partial f}}{{\partial \bar z}} = 0\) throughout an open set Ω ⊆ ℂ. As an immediate consequence of the topological tools developed in that chapter we found that the holomorphic functions enjoyed the following remarkable property (Cauchy’s theorem 1.1 1.4).


Holomorphic Function Entire Function Analytic Property Jordan Curve Jordan Domain 
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Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • Carlos A. Berenstein
    • 1
  • Roger Gay
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsUniversity of BordeauxTalenceFrance

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