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# Function Theory of Several Complex Variables

564 pages, parution le 01/08/2001 (2eme édition)

## Résumé

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.

It is currently the only book on the subject with exercises and a large number of examples.

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

## L'auteur - Steven G. Krantz

Steven G. Krantz, currently Professor and Chairman of Mathematics at Washington University in St. Louis, earned his PhD at Princeton University and has taught at UCLA, Princeton University and Pennsylvania State University. He is the recipient of the UCLA Alumni Foundation Distinguished Teaching Award, the MAA's Chauvenet Prize, the MAA Beckenbach Book Award, and the Outstanding Academic Book Award of the Current Review of Academic Libraries. He has written numerous books including: "Function Theory of Several Complex Variables," "Real Analysis and Foundations," "The Geometry of Domains in Space" (with Harold R. Parks), "Function Theory of One Complex Variable" (with Robert E. Greene), "The Implicit Function Theorem" (with Harold Parks). "Complex Analysis: The Geometric Viewpoint," and" A Panorama of Harmonic Analysis" (both for the MAA). He is also the author of over one-hundred research articles.

## Caractéristiques techniques

 PAPIER Éditeur(s) American Mathematical Society (AMS) Auteur(s) Steven G. Krantz Parution 01/08/2001 Édition 2eme édition Nb. de pages 564 Couverture Relié EAN13 9780821827246 ISBN13 978-0-8218-2724-6

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