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Function Theory of Several Complex Variables: Second Edition
 
Steven G. Krantz Washington University, St. Louis, MO
Function Theory of Several Complex Variables
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
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
Function Theory of Several Complex Variables
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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
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
  • 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.

    Readership

    Graduate 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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