Abstract
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].
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