AMS Chelsea Publishing 1992; 564 pp; hardcover Volume: 340 ISBN10: 0821827243 ISBN13: 9780821827246 List Price: US$64 Member Price: US$57.60 Order Code: CHEL/340.H
 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 (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. Readership Graduate students and research mathematicians interested in several complex variables and analytic spaces. Reviews "This book makes available a comprehensive, detailed and carefully organized treatment of the foundations for multidimensional complex analysis. ...provides all sorts of topics and exercises which stretch the imagination and show how useful the subject really is."  Zentralblatt MATH "One of the remarkable features of this book is that it contains a large number of exercises and problems. ...the student needs a book like Krantz's, which is written as a text with explainations and exercises."  Bulletin of the American Mathematical Society Table of Contents  An introduction to the subject
 Some integral formulas
 Subharmonicity and its applications
 Convexity
 Hörmander's solution of the \(\bar\partial\) equation
 Solution of the Levi problem and other applications of \(\bar\partial\) techniques
 Cousin problems, cohomology, and sheaves
 The zero set of a holomorphic function
 Some harmonic analysis
 Constructive methods
 Integral formulas for solutions to the \(\bar\partial\) problem and norm estimates
 Holomorphic mappings and invariant metrics
 Manifolds
 Area measures
 Exterior algebra
 Vectors, covectors, and differential forms
 List of notation
 Bibliography
 Index
