Hardcover ISBN:  9780821827246 
Product Code:  CHEL/340.H 
564 pp 
List Price:  $64.00 
MAA Member Price:  $57.60 
AMS Member Price:  $57.60 
Electronic ISBN:  9781470429911 
Product Code:  CHEL/340.H.E 
564 pp 
List Price:  $64.00 
MAA Member Price:  $57.60 
AMS Member Price:  $57.60 

Book DetailsAMS Chelsea PublishingVolume: 340; 1992MSC: 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.

Table of Contents

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


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 Get Permissions
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