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Function Theory of Several Complex Variables
Publisher: American Mathematical Society
Number Of Pages: 564
Publication Date: 2001-01-01
Sales Rank: 783742
ISBN / ASIN: 0821827243
EAN: 9780821827246
Binding: Hardcover
Manufacturer: American Mathematical Society
Studio: American Mathematical Society
Average Rating: 5
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.
It is currently the only book on the subject with exercises and a large number of examples.
Review:
readable and engaging, good introduction to subject
Krantz has a very readable style and this is one math book that is fun reading (assuming you have the background listed above). No definition causes you to wonder why it was defined, and no theorem causes you to wonder why it was proved.
It's also one of the few books that defines sheaf cohomology in terms of actual geometric intuition and concrete examples. Even readers not interested in several complex variables should benefit from the way he treats tangential subjects in this book.
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