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The Cauchy-Riemann Complex: Integral Formulae and Neumann Problem

✍ Scribed by Prof. Dr. Ingo Lieb, Prof. Dr. Joachim Michel (auth.)

Publisher
Vieweg+Teubner Verlag
Year
2002
Tongue
English
Leaves
363
Series
Aspects of Mathematics 34
Edition
1
Category
Library
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✦ Synopsis

The method of integral representations is developed in order to establish 1. classical fundamental results of complex analysis both elementary and advanced, 2. subtle existence and regularity theorems for the Cauchy-Riemann equations on complex manifolds. These results are then applied to important function theoretic questions. The book can be used for advanced courses and seminars at the graduate level; it contains to a large extent material which has not yet been covered in text books.

✦ Table of Contents

Front Matter....Pages I-X
Introduction....Pages 1-7
The Bochner-Martinelli-Koppelman Formula....Pages 9-57
The Calculus of Cauchy-Fantappiè Forms....Pages 59-72
Strictly Pseudoconvex Domains in β„‚ n ....Pages 73-127
Strictly Pseudoconvex Manifolds....Pages 129-181
The $$ % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafyOaIyRbae % baaaa!376B! \bar \partial $$ -Neumann Problem....Pages 183-210
Integral Representations for the $$ % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafyOaIyRbae % baaaa!376B! \bar \partial $$ -Neumann Problem....Pages 211-253
Regularity Properties of Admissible Operators....Pages 255-299
Regularity of the $$ % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafyOaIyRbae % baaaa!376B! \bar \partial $$ -Neumann Problem and Applications....Pages 301-335
Back Matter....Pages 337-362

✦ Subjects

Partial Differential Equations; Analysis

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