Polynomial Convexity [electronic resource] / by Edgar Lee Stout.

By: Stout, Edgar Lee [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Progress in Mathematics: 261Publisher: Boston, MA : Birkhäuser Boston, 2007Description: X, 439 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817645380Subject(s): Mathematics | Algebra | Field theory (Physics) | Mathematical analysis | Analysis (Mathematics) | Functional analysis | Functions of complex variables | Mathematics | Several Complex Variables and Analytic Spaces | Functions of a Complex Variable | Field Theory and Polynomials | Functional Analysis | AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515.94 LOC classification: QA331.7Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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.

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