Edgar Lee Stout
Birkhäuser Boston
2007e druk, 2007
9780817645373
Polynomial Convexity
Specificaties
Gebonden, 439 blz.
|
Engels
Birkhäuser Boston |
2007e druk, 2007
ISBN13: 9780817645373
Rubricering
Onderdeel van serie
Progress in Mathematics
Levertijd ongeveer 8 werkdagen
Samenvatting
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.
Specificaties
ISBN13:9780817645373
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:439
Uitgever:Birkhäuser Boston
Druk:2007
Serie:Progress in Mathematics
Inhoudsopgave
Preface.
Introduction. Polynomial convexity. Uniform algebras. Plurisubharmonic fuctions. The Cauchy-Fantappiè 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.
Introduction. Polynomial convexity. Uniform algebras. Plurisubharmonic fuctions. The Cauchy-Fantappiè 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.