Holomorphic functions and integral representations in several complex variables

Description:

This is an introductory text in several complex variables, using methods of integral representations. It begins with elementary local results, discusses basic new concepts of the multi-dimensional theory such as pseudoconvexity and holomorphic convexity, and leads up to complete proofs of fundamental global results, both classical and new. The use of integral representation techniques makes it possible to treat the subject with a minimum of prerequisites, and it has the further advantage that it uses the multivariable forms of theorem with which the students are already acquainted. This book also provides a systematic introduction to integral representation methods and their applications, including a simplified proof of C. Fefferman's famous mapping theorem.

subjects: Functions of several complex variables,  Holomorphic functions,  Integral representations,  Représentations intégrales,  Fonction holomorphe,  Représentation intégrale,  Holomorphe Funktion,  Holomorphie,  Problème Levi,  Fonctions holomorphes,  Fonction variable complexe,  Fonctions de plusieurs variables complexes,  Pseudo-convexité,  Fonction à plusieurs variables,  Mathematics,  Global analysis (Mathematics),  Analysis