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Holomorphic Functions and Integral Representations in Several Complex Variables (Hardcover, 1st ed. 1986. Corr. 2nd printing 1998)
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Holomorphic Functions and Integral Representations in Several Complex Variables (Hardcover, 1st ed. 1986. Corr. 2nd printing 1998)
Series: Graduate Texts in Mathematics, 108
Expected to ship within 12 - 17 working days
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The subject of this book is Complex Analysis in Several Variables.
This text begins at an elementary level with standard local
results, followed by a thorough discussion of the various
fundamental concepts of "complex convexity" related to the
remarkable extension properties of holomorphic functions in more
than one variable. It then continues with a comprehensive
introduction to integral representations, and concludes with
complete proofs of substantial global results on domains of
holomorphy and on strictly pseudoconvex domains inC," including,
for example, C. Fefferman's famous Mapping Theorem. The most
important new feature of this book is the systematic inclusion of
many of the developments of the last 20 years which centered around
integral representations and estimates for the Cauchy-Riemann
equations. In particu lar, integral representations are the
principal tool used to develop the global theory, in contrast to
many earlier books on the subject which involved methods from
commutative algebra and sheaf theory, and/or partial differ ential
equations. I believe that this approach offers several advantages:
(1) it uses the several variable version of tools familiar to the
analyst in one complex variable, and therefore helps to bridge the
often perceived gap between com plex analysis in one and in several
variables; (2) it leads quite directly to deep global results
without introducing a lot of new machinery; and (3) concrete
integral representations lend themselves to estimations, therefore
opening the door to applications not accessible by the earlier
methods."
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