| Hardcover ISBN: | 978-0-8218-2724-6 |
| Product Code: | CHEL/340.H |
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| MAA Member Price: | $62.10 |
| AMS Member Price: | $62.10 |
| eBook ISBN: | 978-1-4704-2991-1 |
| Product Code: | CHEL/340.H.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $58.50 |
| Hardcover ISBN: | 978-0-8218-2724-6 |
| eBook: ISBN: | 978-1-4704-2991-1 |
| Product Code: | CHEL/340.H.B |
| List Price: | $134.00 $101.50 |
| MAA Member Price: | $120.60 $91.35 |
| AMS Member Price: | $120.60 $91.35 |
| Hardcover ISBN: | 978-0-8218-2724-6 |
| Product Code: | CHEL/340.H |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $62.10 |
| eBook ISBN: | 978-1-4704-2991-1 |
| Product Code: | CHEL/340.H.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $58.50 |
| Hardcover ISBN: | 978-0-8218-2724-6 |
| eBook ISBN: | 978-1-4704-2991-1 |
| Product Code: | CHEL/340.H.B |
| List Price: | $134.00 $101.50 |
| MAA Member Price: | $120.60 $91.35 |
| AMS Member Price: | $120.60 $91.35 |
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Book DetailsAMS Chelsea PublishingVolume: 340; 1992; 564 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in several complex variables and analytic spaces.
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Table of Contents
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Chapters
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Chapter 0. An introduction to the subject
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Chapter 1. Some integral formulas
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Chapter 2. Subharmonicity and its applications
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Chapter 3. Convexity
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Chapter 4. Hörmander’s solution of the $\bar \partial $ equation
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Chapter 5. Solution of the Levi problem and other applications of $\bar \partial $ techniques
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Chapter 6. Cousin problems, cohomology, and sheaves
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Chapter 7. The zero set of a holomorphic function
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Chapter 8. Some harmonic analysis
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Chapter 9. Constructive methods
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Chapter 10. Integral formulas for solutions to the $\bar \partial $ problem and norm estimates
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Chapter 11. Holomorphic mappings and invariant metrics
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Appendix I. Manifolds
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Appendix II. Area measures
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Appendix III. Exterior algebra
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Appendix IV. Vectors, covectors, and differential forms
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
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
