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The Cauchy-Riemann Complex: Integral Formulae and Neumann Problem
Ingo Lieb, Universität Bonn, Germany, and Joachim Michel, Université du Littoral, Calais, France
A publication of Vieweg+Teubner.
Vieweg Aspects of Mathematics
2002; 362 pp; hardcover
Volume: 34
ISBN-10: 3-528-06954-6
ISBN-13: 978-3-528-06954-4
List Price: US$109
Member Price: US$98.10
Order Code: VWAM/34
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Distributed by the AMS for the respected publishing house of Vieweg Verlag, this book presents complex analysis of several variables from the point of view of Cauchy-Riemann equations and integral representations. Some of the material has not yet been covered in other texts.

The method of integral representations is developed to establish classical results of complex analysis, both elementary and advanced, as well as subtle existence and regularity theorems for Cauchy-Riemann equations on complex manifolds. These results are applied to important questions in function theory.

Prerequisites for reading the text are basic theory of functions of several complex variables and a strong background in classical analysis, in particular distributions and integration theory. The book is a suitable text for advanced graduate courses and research seminars on several complex variables.

A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan.


Graduate students and research mathematicians interested in several complex variables.

Table of Contents

  • Introduction
  • The Bochner-Martinelli-Koppelman formula
  • Cauchy-Fantappiè forms
  • Strictly pseudoconvex domains in \(\mathbb{C}^n\)
  • Strictly pseudoconvex manifolds
  • The \(\overline\partial\)-Neumann problem
  • Integral representations for the \(\overline\partial\)-Neumann problem
  • Regularity properties of admissible operators
  • Regularity of the \(\overline\partial\)-Neumann problem and applications
  • Bibliography
  • Notations
  • Index
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