Holomorphic functions and integral representations in several complex variables

the long version

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.