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the cauchy-riemann complex: integral formulae & Neumann Ingo Lieb [PDF]

# The Cauchy-Riemann Complex: Integral Formulae & Neumann Problem by Ingo Lieb, Joachim Michel

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The Cauchy-Riemann Complex: Integral Formulae & Neumann Problem written by Ingo Lieb, Joachim Michel.
This book presents complex analysis of several variables from the point of view of the Cauchy-Riemann equations and integral representations. A more detailed description of our methods and main results can be found in the introduction. Here we only make some remarks on our aims and on the required background knowledge.
Integral representation methods serve a twofold purpose: 1° they yield regularity results not easily obtained by other methods and 2°, along the way, they lead to a fairly simple development of parts of the classical theory of several complex variables. We try to reach both aims. Thus, the first three to four chapters, if complemented by an elementary chapter on holomorphic functions, can be used by a lecturer as an introductory course to complex analysis. They contain standard applications of the Bochner-Martinelli-Koppelman integral representation, a complete presentation of Cauchy-Fantappie forms giving also the numerical constants of the theory, and a direct study of the Cauchy-Riemann complex on strictly pseudoconvex domains leading, among other things, to a rather elementary solution of Levi's problem in complex number space en.

Book Detail :-
Title: The Cauchy-Riemann Complex: Integral Formulae & Neumann Problem
Edition:
Author(s): Ingo Lieb, Joachim Michel
Publisher: Vieweg+Teubner Verlag
Series: Aspects of Mathematics 34
Year: 2002
Pages: 363
Type: PDF
Language: English
ISBN: 978-3-322-91610-5,978-3-322-91608-2
Country: Germany, French
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About Author :- The author Prof. Dr. Jngo Lieb , Rheinische Friedrich-Wilhelms-Universitat Bonn, Mathematisches Institut, BeringstraBe 6, D-53115 Bonn, Germany. The author Prof. Dr. Joachim Michel , Laboratoire de Mathematiques Pures et, Appliquees Joseph Liouville, 50, rue Ferdinand Buisson, F-62228 Calais Cedex, France.

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Book Contents :-
The Cauchy-Riemann Complex: Integral Formulae & Neumann Problem written by Ingo Lieb, Joachim Michel cover the following topics.
Introduction
1. The Bochner-Martinelli-Koppelman Formula
2. Cauchy-Fantappie Forms
3. Strictly Pseudoconvex Domains in en
4. Strictly Pseudoconvex Manifolds
5. The a-Neumann Problem
6. Integral Representations for the a-Neumann Problem
7. Regularity Properties of Admissible Operators
Bibliography
Notations
Index

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