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 $L $ extension theorem
for holomorphic functions, that have 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 is assumed that the reader has a basic knowledge of complex
analysis at the undergraduate level. The book would make a suitable
supplementary text for a graduate-level course on complex analysis.
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