Several Complex Variables and Integral Formulas~tqw~ darksiderg

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Several Complex Variables and Integral Formulas
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Release NotesThis volume is an introductory text in several complex variables, using methods
of integral representations and Hilbert space theory. It investigates mainly the
studies of the estimate of solutions of the Cauchy-Riemann equations in
pseudoconvex domains and the extension of holomorphic functions in submanifolds
of pseudoconvex domains which were developed in the last 50 years. We discuss
the two main studies mentioned above by two different methods: the integral
formulas and the Hilbert space techniques. The theorems concerning general
pseudoconvex domains are analyzed using Hilbert space theory, and the proofs for
theorems concerning strictly pseudoconvex domains are solved using integral
representations.

This volume is written in a self-contained style, so that the proofs are easily
accessible to beginners. There are exercises featured at the end of each chapter
to aid readers to better understand the materials of this volume. Fairly
detailed hints are articulated to solve these exercises.

Table Of Contents

Preface vii
1. Pseudoconvexity and Plurisubharmonicity
2. The P