**AMS Chelsea Publishing**

Volume: 340;
1992;
564 pp;
Hardcover

MSC: Primary 32;
Secondary 35

Print ISBN: 978-0-8218-2724-6

Product Code: CHEL/340.H

List Price: $64.00

AMS Member Price: $57.60

MAA member Price: $57.60

**Electronic ISBN: 978-1-4704-2991-1
Product Code: CHEL/340.H.E**

List Price: $64.00

AMS Member Price: $57.60

MAA member Price: $57.60

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# Function Theory of Several Complex Variables: Second Edition

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*Steven G. Krantz*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Function Theory of Several Complex Variables: Second Edition

- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface to the second edition xiii14
- Preface to the first edition xv16
- An introduction to the subject 118
- Some integral formulas 1936
- Subharmonicity and its applications 8198
- Convexity 117134
- Hörmander’s solution of the ∂ equation 175192
- Solution of the Levi problem and other applications of ∂ techniques 213230
- Cousin problems, cohomology, and sheaves 243260
- The zero set of a holomorphic function 293310
- Some harmonic analysis 321338
- Constructive methods 381398
- Integral formulas for solutions to the ∂ problem and norm estimates 403420
- Holomorphic mappings and invariant metrics 429446
- Appendix I. Manifolds 493510
- Appendix II. Area measures 495512
- Appendix III. Exterior algebra 499516
- Appendix IV. Vectors, covectors, and differential forms 503520
- List of notation 509526
- Bibliography 515532
- Index 553570
- Back Cover Back Cover1586