Progress in Mathematics

Polynomial Convexity

Authors: Stout, Edgar Lee

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  • Offers a distinctive and comprehensive approach to the theory of polynomially convex sets
  • Packed with examples and counterexamples to illustrate complex ideas
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About this book

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.

Reviews

From the reviews:

"The style is rigorous, elegant and clear, the exposition is beautiful. The book is an extremely important tool to every researcher interested in the subject, as it contains basic facts and therefore will remain a standard reference in the future and, moreover, it opens a perspective on further directions of research."—Zentralblatt Math

"This is an excellent … introductory book for researchers in complex function theory and approximation theory that certainly becomes one of the chief references for these topics. I think the importance and main techniques of how to use polynomial convexity as a standard tool is rather clear for the mentioned experts. … The book is highly recommended for every researcher and postgraduate student working in areas with intensive use of complex analysis, analytic varieties or approximation theory." (László Stachó, Acta Scientiarum Mathematicarum, Vol. 74, 2008)

“Polynomial convexity is an important concept in the theory of functions of several complex variables, especially for approximation. This excellent exposition of a rich theory presents the general properties of polynomially convex sets with attention to hulls of one-dimensional sets … . Together with the comprehensive bibliography and the numerous interesting historical remarks this book will serve as a standard reference for many years.” (F. Haslinger, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-0-8176-4538-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-0-8176-4537-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Polynomial Convexity
Authors
Series Title
Progress in Mathematics
Series Volume
261
Copyright
2007
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4538-0
DOI
10.1007/978-0-8176-4538-0
Hardcover ISBN
978-0-8176-4537-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
X, 439
Topics