Overview
This book is devoted to an exposition of the theory of polynomially convex sets.Acompact N subset of C is polynomially convex if it is de?ned by a family, ?nite or in?nite, of polynomial inequalities. These sets play an important role in the theory of functions of several complex variables, especially in questions concerning approximation. On the one hand, the present volume is a study of polynomial convexity per se, on the other, it studies the application of polynomial convexity to other parts of complex analysis, especially to approximation theory and the theory of varieties. N Not every compact subset of C is polynomially convex, but associated with an arbitrary compact set, say X, is its polynomially convex hull, X, which is the intersection of all polynomially convex sets that contain X. Of paramount importance in the study of polynomial convexity is the study of the complementary set X \ X. The only obvious reason for this set to be nonempty is for it to have some kind of analytic structure, and initially one wonders whether this set always has complex structure in some sense. It is not long before one is disabused of this naive hope; a natural problem then is that of giving conditions under which the complementary set does have complex structure. In a natural class of one-dimensional examples, such analytic structure is found. The study of this class of examples is one of the major directions of the work at hand.
Full Product Details
Author: Edgar Lee Stout
Publisher: Birkhauser Boston Inc
Imprint: Birkhauser Boston Inc
Edition: 2007 ed.
Volume: 261
Dimensions:
Width: 15.50cm
, Height: 2.50cm
, Length: 23.50cm
Weight: 0.852kg
ISBN: 9780817645373
ISBN 10: 0817645373
Pages: 439
Publication Date: 03 May 2007
Audience:
Professional and scholarly
,
College/higher education
,
Professional & Vocational
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: In Print
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Reviews
From the reviews: <p> 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. a Zentralblatt Math <p> This is an excellent a ] 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. a ] 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. (LAszlA3 StachA3, Acta Scientiarum Mathematicarum, Vol. 74, 2008)
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. (Laszlo Stacho, Acta Scientiarum Mathematicarum, Vol. 74, 2008)
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. (Laszlo Stacho, 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 fur Mathematik, Vol. 156 (4), April, 2009)
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. (Laszlo Stacho, 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 fur Mathematik, Vol. 156 (4), April, 2009)
