Overview

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. Polynomial Convexity : includes 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; and 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. It also discusses important applications, e.g., to the study of analytic varieties and to the theory of removable singularities for CR functions; and 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 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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9786610956739

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