Edgar Lee Stout

Polynomial Convexity (eBook, PDF)

• Format: PDF

Produktbeschreibung

This comprehensive monograph is devoted to the study of polynomially convex sets, which play a key role in the theory of functions of several complex variables. The presentation includes the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. The theory is motivated with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries. This beautiful exposition of a rich and complex theory, which contains much material not available in other texts and which is destined to be the standard reference for many years, will appeal to all those with an interest in multivariate complex analysis.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 439
• Erscheinungstermin: 28. Juli 2007
• Englisch
• ISBN-13: 9780817645380
• Artikelnr.: 37339545

Autorenporträt

Edgar Lee Stout, University of Washington, Seattle, USA

Inhaltsangabe

Some General Properties of Polynomially Convex Sets.- Sets of Finite Length.- Sets of Class A1.- Further Results.- Approximation.- Varieties in Strictly Pseudoconvex Domains.- Examples and Counterexamples.

Rezensionen

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)