Tópicos sobre funções de várias variáveis complexas - Coacalle, Joel Rogelio Portada (2015)
This work shows classical results of analysis of holomorphic functions of both one and several complex variables. Are treated as main topics results on integral representations of holomorphic functions, approximation by holomomorfas functions, the Cauchy-Riemman operator and its homogeneous and non homogeneous equation associated, results on func- tions subharmonics, and the problem of analytic continuation. As the integral representa- tion of holomorphic functions present the Cauchy Integral Formula well as the immediate results of this as are the representation in series of powers, estimates of Cauchy and the most important of the principle for holomorphic functions, these results as much as for one and several complex variables. As the approach we present here the Runge theorem, as well as those resulting from its application in the context of meromorphic functions that are Mittag-Leffler's theorem and the Weierstrass theorem. Subharmonic functions are handled here putting out two main properties and some others that can be seen even in a generalized sense. As for analytic continuation of problems discussed here in the context of several complex variables Hartog the Extension Theorem, some geometric pro- perties of holomorphy domains where we prove a special case where analytical extension called Bochner's theorem, the special case of a domain named Domain Reinhardt, and some properties on the concepts of plurisubharmonicidade and pseudoconvexidade.