Function Theory of Several Complex Variables

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American Mathematical Soc., 2001 - Mathematics - 564 pages
This work departs from earlier treatments of the subject by emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and mapping theory. While due homage is paid to the more traditional algebraic theory (for example, sheaves, and Cousin problems), the student with a background in real and complex variable theory, harmonic analysis, and differential equations should be most comfortable with this treatment.


Title page
Preface to the second edition
Preface to the first edition
An introduction to the subject
Some integral formulas
Some harmonic analysis
Constructive methods
Integral formulas for solutions to the problem and norm estimates
Holomorphic mappings and invariant metrics
Appendix I Manifolds
Appendix II Area measures
Appendix III Exterior algebra
Appendix IV Vectors covectors and differential forms

Subharmonicity and its applications
Hörmanders solution of the equation
Solution of the Levi problem and other applications of techniques
Cousin problems cohomology and sheaves
The zero set of a holomorphic function
List of notation
Back Cover

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About the author (2001)

Steven G. Krantz is an accomplished mathematician and an award-winning author. He has published more than 150 research articles and over 50 books. He has worked as an editor of several book series, research journals, and for the Notices of the AMS.

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