Function Theory in the Unit Ball of ℂn

  • Walter Rudin

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 241)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Walter Rudin
    Pages 1-22
  3. Walter Rudin
    Pages 23-35
  4. Walter Rudin
    Pages 36-46
  5. Walter Rudin
    Pages 47-64
  6. Walter Rudin
    Pages 65-90
  7. Walter Rudin
    Pages 91-119
  8. Walter Rudin
    Pages 120-160
  9. Walter Rudin
    Pages 161-184
  10. Walter Rudin
    Pages 185-203
  11. Walter Rudin
    Pages 204-233
  12. Walter Rudin
    Pages 234-252
  13. Walter Rudin
    Pages 253-277
  14. Walter Rudin
    Pages 278-287
  15. Walter Rudin
    Pages 288-299
  16. Walter Rudin
    Pages 300-329
  17. Walter Rudin
    Pages 330-363
  18. Walter Rudin
    Pages 364-386
  19. Walter Rudin
    Pages 387-402
  20. Walter Rudin
    Pages 403-417

About this book

Introduction

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.

Keywords

Function Funktionentheorie Smooth function complex analysis convergence differential equation holomorphic function integral interpolation maximum minimum operator

Authors and affiliations

  • Walter Rudin
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8098-6
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8100-6
  • Online ISBN 978-1-4613-8098-6
  • Series Print ISSN 0072-7830
  • About this book
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