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Function Theory of Several Complex Variables: Second Edition

Steven G. Krantz Washington University, St. Louis, MO
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-0-8218-2724-6
Product Code: CHEL/340.H
List Price: $64.00 MAA Member Price:$57.60
AMS Member Price: $57.60 Electronic ISBN: 978-1-4704-2991-1 Product Code: CHEL/340.H.E List Price:$64.00
MAA Member Price: $57.60 AMS Member Price:$57.60
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List Price: $96.00 MAA Member Price:$86.40
AMS Member Price: $86.40 Click above image for expanded view Function Theory of Several Complex Variables: Second Edition Steven G. Krantz Washington University, St. Louis, MO AMS Chelsea Publishing: An Imprint of the American Mathematical Society Available Formats:  Hardcover ISBN: 978-0-8218-2724-6 Product Code: CHEL/340.H  List Price:$64.00 MAA Member Price: $57.60 AMS Member Price:$57.60
 Electronic ISBN: 978-1-4704-2991-1 Product Code: CHEL/340.H.E
 List Price: $64.00 MAA Member Price:$57.60 AMS Member Price: $57.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$96.00 MAA Member Price: $86.40 AMS Member Price:$86.40
• Book Details

AMS Chelsea Publishing
Volume: 3401992; 564 pp
MSC: Primary 32; Secondary 35;

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.

Graduate students and research mathematicians interested in several complex variables and analytic spaces.

• Chapters
• Chapter 0. An introduction to the subject
• Chapter 1. Some integral formulas
• Chapter 2. Subharmonicity and its applications
• Chapter 3. Convexity
• Chapter 4. Hörmander’s solution of the $\bar \partial$ equation
• Chapter 5. Solution of the Levi problem and other applications of $\bar \partial$ techniques
• Chapter 6. Cousin problems, cohomology, and sheaves
• Chapter 7. The zero set of a holomorphic function
• Chapter 8. Some harmonic analysis
• Chapter 9. Constructive methods
• Chapter 10. Integral formulas for solutions to the $\bar \partial$ problem and norm estimates
• Chapter 11. Holomorphic mappings and invariant metrics
• Appendix I. Manifolds
• Appendix II. Area measures
• Appendix III. Exterior algebra
• Appendix IV. Vectors, covectors, and differential forms
• 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
• Request Review Copy
• Get Permissions
Volume: 3401992; 564 pp
MSC: Primary 32; Secondary 35;

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.

Graduate students and research mathematicians interested in several complex variables and analytic spaces.

• Chapters
• Chapter 0. An introduction to the subject
• Chapter 1. Some integral formulas
• Chapter 2. Subharmonicity and its applications
• Chapter 3. Convexity
• Chapter 4. Hörmander’s solution of the $\bar \partial$ equation
• Chapter 5. Solution of the Levi problem and other applications of $\bar \partial$ techniques
• Chapter 6. Cousin problems, cohomology, and sheaves
• Chapter 7. The zero set of a holomorphic function
• Chapter 8. Some harmonic analysis
• Chapter 9. Constructive methods
• Chapter 10. Integral formulas for solutions to the $\bar \partial$ problem and norm estimates
• Chapter 11. Holomorphic mappings and invariant metrics
• Appendix I. Manifolds
• Appendix II. Area measures
• Appendix III. Exterior algebra
• Appendix IV. Vectors, covectors, and differential forms
• 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
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