Edgar Lee Stout (auth.)0817645373, 9780817645373, 9780817645380
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.
Table of contents :
Front Matter….Pages i-xi
Introduction….Pages 1-70
Some General Properties of Polynomially Convex Sets….Pages 71-120
Sets of Finite Length….Pages 121-168
Sets of Class A 1 ….Pages 169-216
Further Results….Pages 217-276
Approximation….Pages 277-350
Varieties in Strictly Pseudoconvex Domains….Pages 351-376
Examples and Counterexamples….Pages 377-414
Back Matter….Pages 415-439
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