Function Theory of Several Complex Variables

This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory.

Authors: Noguchi, Junjiro
Is an easily readable and enjoyable text on the classical analytic function theory of several complex variables for new graduate students in mathematics
Includes complete proofs of Oka's Three Coherence Theorems, Oka–Cartan's Fundamental Theorem, and Oka's Theorem on Levi's problem for Riemann domains
Can easily be used for courses and lectures with self-contained treatments and a number of simplifications of classical proofs

The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps).