Function Theory of Several Complex Variables

Steven G. Krantz

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

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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	2^eme édition
Nb. de pages	564
Couverture	Relié
EAN13	9780821827246
ISBN13	978-0-8218-2724-6