Polynomial convexity

Author(s)

• Stout, Edgar Lee

Bibliographic Information

Polynomial convexity

Edgar Lee Stout

（Progress in mathematics, v. 261）

Birkhäuser, c2007

Note

Includes bibliographical references (p. [415]-429) and index

Description and Table of Contents

Description

This comprehensive monograph details polynomially convex sets. It presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of one-dimensional sets. Coverage examines in considerable detail questions of uniform approximation for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. The book also discusses important applications and motivates the reader with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries.

Table of Contents

Preface. Introduction. Polynomial convexity. Uniform algebras. Plurisubharmonic fuctions. The Cauchy-Fantappie Integral. The Oka-Weil Theorem. Some examples. Hulls with no analytic structure.- Some General Properties of Polynomially Convex Sets. Applications of the Cousin problems. Two characterizations of polynomially convex sets. Applications of Morse theory and algebraic topology. Convexity in Stein manifolds.- Sets of Finite Length. Introduction. One-dimensional varieties. Geometric preliminaries. Function-theoretic preliminaries. Subharmonicity results. Analytic structure in hulls. Finite area. The continuation of varieties.- Sets of Class A1. Introductory remarks. Measure-theoretic preliminaries. Sets of class A1. Finite area. Stokes's Theorem. The multiplicity function. Counting the branches.- Further Results. Isoperimetry. Removable singularities. Surfaces in strictly pseudoconvex boundaries.- Approximation. Totally real manifolds. Holomorphically convex sets. Approximation on totally real manifolds. Some tools from rational approximation. Algebras on surfaces. Tangential approximation.- Varieties in Strictly Pseudoconvex Domains. Interpolation. Boundary regularity. Uniqueness.- Examples and Counter Examples. Unions of planes and balls. Pluripolar graphs. Deformations. Sets with symmetry.- Bibliography. Index.

by "Nielsen BookData"

Details

• NCID: BA82070067
• ISBN:
  • 9780817645373
• LCCN: 2007923422
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boston
• Pages/Volumes: x, 439 p.
• Size: 24 cm
• Classification:
  • SG : 510
• Subject Headings:
  • LCSH : Functions of several complex variables
  • LCSH : Polynomials
• Parent Bibliography ID:
  • BA00018010