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Polynomial Convexity

  • Edgar Lee Stout

Part of the Progress in Mathematics book series (PM, volume 261)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 1-70
  3. Pages 121-168
  4. Pages 169-216
  5. Pages 217-276
  6. Pages 277-350
  7. Back Matter
    Pages 415-439

About this book

Introduction

This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables.

Important features of Polynomial Convexity:

*Presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets.

*Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.

*Examines in considerable detail questions of uniform approximation, especially on totally real sets, for the most part on compact sets but with some attention to questions of global approximation on noncompact sets.

*Discusses important applications, e.g., to the study of analytic varieties and to the theory of removable singularities for CR functions.

*Requires of the reader a solid background in real and complex analysis together with some previous experience with the theory of functions of several complex variables as well as the elements of functional analysis.

This beautiful exposition of a rich and complex theory, which contains much material not available in other texts, is destined to be the standard reference for many years, and will appeal to all those with an interest in multivariate complex analysis.

Keywords

Complex analysis Convexity Pseudoconvexity convex hull functional analysis polynomial convexity polynomial hulls subharmonic function

Authors and affiliations

  • Edgar Lee Stout
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4538-0
  • Copyright Information Birkhäuser Boston 2007
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4537-3
  • Online ISBN 978-0-8176-4538-0
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site