The \(\bar \partial\)-Equation

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


It is in this chapter that the difference between our textbook and more classical ones appears markedly. As stated in the preface, we have attempted to use, as systematically as possible, the inhomogeneous Cauchy-Riemann equation \(\frac{{\partial f}}{{\partial \bar z}} = g\) to study holomorphic functions (also called \(\bar \partial\)-equation). The reader should note the irony here. To better comprehend the solutions of the homogeneous equation \(\frac{{\partial f}}{{\partial \bar z}} = 0\) one is forced to study a more complex object! Our presentation owes much to Hörmander’s beautiful treatise on several complex variables [Ho1].


Compact Subset Holomorphic Function Entire Function Analytic Continuation Meromorphic Function 
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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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