Polynomial Convexity
Stout, Edgar Lee.
creator
author.
SpringerLink (Online service)
text
xxu
2007
monographic
eng
access
X, 439 p. online resource.
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.
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.
by Edgar Lee Stout.
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
Analysis
QA331.7
515.94
Springer eBooks
Progress in Mathematics ; 261
9780817645380
http://dx.doi.org/10.1007/978-0-8176-4538-0
http://dx.doi.org/10.1007/978-0-8176-4538-0
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