One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the Cauchy-Riemann equations). Emphasis is on recent results, including an $L2$ extension theorem for holomorphic functions, thathave brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, topics covered in the book are at the intersection of the theory of analytic functions of several variables and mathematical analysis. It isassumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduate-level course on complex analysis.
Description:
One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the Cauchy-Riemann equations). Emphasis is on recent results, including an $L2$ extension theorem for holomorphic functions, thathave brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, topics covered in the book are at the intersection of the theory of analytic functions of several variables and mathematical analysis. It isassumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduate-level course on complex analysis.