Grundlehren der mathematischen Wissenschaften

Function Theory in the Unit Ball of ℂn

Authors: Rudin, W.

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About this book

Around 1970, an abrupt change occurred in the study of holomorphic functions of several complex variables. Sheaves vanished into the back­ ground, and attention was focused on integral formulas and on the "hard analysis" problems that could be attacked with them: boundary behavior, complex-tangential phenomena, solutions of the J-problem with control over growth and smoothness, quantitative theorems about zero-varieties, and so on. The present book describes some of these developments in the simple setting of the unit ball of en. There are several reasons for choosing the ball for our principal stage. The ball is the prototype of two important classes of regions that have been studied in depth, namely the strictly pseudoconvex domains and the bounded symmetric ones. The presence of the second structure (i.e., the existence of a transitive group of automorphisms) makes it possible to develop the basic machinery with a minimum of fuss and bother. The principal ideas can be presented quite concretely and explicitly in the ball, and one can quickly arrive at specific theorems of obvious interest. Once one has seen these in this simple context, it should be much easier to learn the more complicated machinery (developed largely by Henkin and his co-workers) that extends them to arbitrary strictly pseudoconvex domains. In some parts of the book (for instance, in Chapters 14-16) it would, however, have been unnatural to confine our attention exclusively to the ball, and no significant simplifications would have resulted from such a restriction.

Table of contents (19 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4613-8098-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Function Theory in the Unit Ball of ℂn
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
241
Copyright
1980
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4613-8098-6
DOI
10.1007/978-1-4613-8098-6
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XIII, 438
Topics