Foundations of complex analysis in non locally convex spaces : function theory without convexity condition /

All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of fun...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bayoumi, Aboubakr
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier, 2003.
Edición:1st ed.
Colección:North-Holland mathematics studies ; v. 193.
Temas:
Holomorphic functions.
Functional analysis.
Convexity spaces.
Convex surfaces.
Complexes.
Fonctions holomorphes.
Analyse fonctionnelle.
Espaces de convexit�e.
Surfaces convexes.
Complexes (Math�ematiques)
MATHEMATICS > Complex Analysis.
Complexes
Convex surfaces
Convexity spaces
Functional analysis
Holomorphic functions
Acceso en línea:Texto completo
Texto completo
Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • Contents
  • CHAPTER 1. FUNDAMENTAL THEOREMS IN F-SPACES
  • 1.1 LINEAR MAPPINGS
  • 1.2 HAHN-BANACH THEOREMS
  • 1.3 OPEN MAPPING THEOREM
  • 1.4 UNIFORM BOUNDEDNESS PRINCIPLE
  • CHAPTER 2. THEORY OF POLYNOMIALS IN F-SPACES
  • 2.1 MULTILINEAR MAPS
  • 2.2 POLYNOMIALS OF P-NORMED SPACES
  • CHAPTER 3. FIXED-POINT AND P-EXTREME POINT
  • 3.1 p-EXTREME POINT IN NON LOCALLY CONVEX SPACES
  • 3.2 GENERALIZED FIXED POINT THEOREM
  • 3.3 GENERALIZED KREIN-MILMAN THEOREM
  • CHAPTER 4. QUASI-DIFFERENTIAL CALCULUS
  • 4.1 QUASI-DIFFERENTIABLE MAPS
  • CHAPTER 5. GENERALIZED MEAN-VALUE THEOREM
  • 5.1 MEAN-VALUE THEOREM IN REAL SPACES
  • 5.2 MEAN-VALUE THEOREM IN COMPLEX SPACES
  • CHAPTER 6. HIGHER QUASI-DIFFERENTIAL IN F-SPACES
  • 6.1 SCHWARTZ SYMMETRIC THEOREM
  • 6.2 HIGHER QUASI-DIFFERENTIALS
  • 6.3 GENERAL SCHWARTZ SYMMETRIC THEOREM
  • 6.4 DIRECTIONAL DERIVATIVES
  • 6.5 QUASI AND FRI�ECHET DIFFERENTIALS
  • CHAPTER 7. QUASI-HOLOMORPHIC MAPS
  • 7.1 FINITE EXPANSIONS AND TAYLOR'S FORMULA
  • 7.2 POWER SERIES IN F-SPACES
  • 7.3 QUASI-ANALYTIC MAPS
  • CHAPTER 8. NEW VERSIONS OF MAIN THEOREMS
  • 8.1 FUNDAMENTAL THEOREM OF CALCULUS
  • 8.2 BOLZANO'S INTERMEDIATE THEOREM
  • 8.3 INTEGRAL MEAN-VALUE THEOREM
  • CHAPTER 9. BOUNDING AND WEAKLY-BOUNDING SETS
  • 9.1 BOUNDING SETS
  • 9.2 WEAKLY-BOUNDING (LIMITED) SETS
  • 9.3 PROPERTIES OF BOUNDING AND LIMITED SETS
  • 9.4 HOLOMORPHIC COMPLETION
  • CHAPTER 10. LEVI PROBLEM IN TOPLOGICAL SPACES
  • 10.1 LEVI PROBLEM AND RADIUS OF CONVERGENCE
  • 10.2 LEVI PROBLEM(GRUMAN-KISELMAN APPROACH)
  • 10.3 LEVI PROBLEM(SURJECTIVE LIMIT APPROACH)
  • 10.4 LEVI PROBLEM(QUOTIENT MAP APPROACH)
  • Bibliography
  • Notations
  • Index
  • Last Page.

Ejemplares similares