Several Complex Variables And Integral Formulas - Kenzo Adachi

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Several Complex Variables And Integral Formulas

By: Kenzo Adachi

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Hardcover | 21 March 2007

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Hardcover
376 Pages

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22.86 x 15.88 x 2.54

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This 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.

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Preface	p. vii
Pseudoconvexity and Plurisubharmonicity	p. 1
The Hartogs Theorem	p. 1
Characterizations of Pseudoconvexity	p. 19
The a Problem in Pseudoconvex Domains	p. 47
The Weighted L[superscript 2] Space	p. 47
L[superscript 2] Estimates in Pseudoconvex Domains	p. 53
The Ohsawa-Takegoshi Extension Theorem	p. 100
Integral Formulas for Strictly Pseudoconvex Domains	p. 117
The Homotopy Formula	p. 117
Holder Estimates for the a Problem	p. 143
Bounded and Continuous Extensions	p. 152
H[superscript p] and C[superscript k] Extensions	p. 183
The Bergman Kernel	p. 196
Fefferman's Mapping Theorem	p. 210
Integral Formulas with Weight Factors	p. 245
The Berndtsson-Andersson Formula	p. 245
L[superscript p] Estimates for the a Problem	p. 255
The Berndtsson Formula	p. 264
Counterexamples for L[superscript p] (p > 2) Extensions	p. 270
Bounded Extensions by Means of the Berndtsson Formula	p. 281
The Classical Theory in Several Complex Variables	p. 291
The Poincare Theorem	p. 291
The Weierstrass Preparation Theorem	p. 298
Oka's Fundamental Theorem	p. 307
The Cousin Problem	p. 326
A Compact Operators	p. 331
B Solutions to the Exercises	p. 343
Bibliography	p. 359
Index	p. 365
Table of Contents provided by Ingram. All Rights Reserved.

Several Complex Variables And Integral Formulas

At a Glance

Hardcover

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Defective items

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