Function Theory of Several Complex VariablesThis 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. |
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Contents
Dedication | |
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 | |
Convexity | |
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 | |
Other editions - View all
Bibliographic information
| Title | Function Theory of Several Complex Variables Volume 340 of AMS Chelsea Publishing Series |
| Author | Steven George Krantz |
| Edition | illustrated |
| Publisher | American Mathematical Soc., 2001 |
| ISBN | 0821827243, 9780821827246 |
| Length | 564 pages |
| Subjects | › Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |