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Analytic Properties of Holomorphic Functions

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

Abstract

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).

Keywords

Holomorphic Function Entire Function Analytic Property Jordan Curve Jordan Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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