Graduate Texts in Mathematics

Holomorphic Functions and Integral Representations in Several Complex Variables

Authors: Range, R. Michael

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About this Textbook

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $69.99
price for USA in USD (gross)
  • ISBN 978-1-4757-1918-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA in USD
  • ISBN 978-0-387-96259-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA in USD
  • ISBN 978-1-4419-3078-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Holomorphic Functions and Integral Representations in Several Complex Variables
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
108
Copyright
1986
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-1918-5
DOI
10.1007/978-1-4757-1918-5
Hardcover ISBN
978-0-387-96259-7
Softcover ISBN
978-1-4419-3078-1
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XX, 392
Topics