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Bayoumi A. — Foundations of Complex Analysis in Non Locally Convex Spaces: Function Theory without Convexity Condition
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Название: Foundations of Complex Analysis in Non Locally Convex Spaces: Function Theory without Convexity ConditionАвтор: Bayoumi A. Аннотация: Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2003Количество страниц: 287Добавлена в каталог: 10.04.2010Операции: Положить на полку |
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Предметный указатель
Affine maps 63 Annhilator of subspace of Metric space 193 Applications to Non-Convex analysis to Operations research 58 Arc segment in Vector space in t.v.s. 50 Baire category theorem 20 Banach Open mapping, p-Banach space 23 Banach — Steinhaus Theorem for Linear maps, Continuous polynomials 25 Banach — Steinhaus type Theorem for Polynomials 46 Bayoumi Space, PB-Space 231 Bayoumi-differentiability, Quasi-differentiability, Interchange order with limit 96 Bolzano Intermediate-Value theorem, Finite and Infinite spaces 163 Bounded approximation property (b.a.p.), Approximation property 186 Bounded Linear map, Norm 3 Bounding sets (Bg), Weakly bounding sets (WBg), Limited sets, Bounded-Weakly bounding sets (B-WBg), Bayoumi Limited set 181 Bounding sets and Holomorphic Completions 220 Bounding sets in Lbs, Bounding sets in F-spaces, Bounding sets in Lps and t.v.s. 186 Bounding sets in Non Lps in t.v.s. 189 Brouwer Fixed point, Generalized 63 Cauchy sequence 5 Cauchy — Hadamard formula, Generalized, Radius of Uniform convergece 139 Cauchy — Hadamard formula, Radius of convergence, Holomorphic function 237 Compact, p-Exteme set, p-Convex set 56 Complemented subspace 244 Completion Linear Holomorphic 207 Complex Mean-Value theorems Mean-Value Inequality 94 Construction of holomorphic maps on locally bounded spaces on Lps F-spaces 199 Continuity of linear map 3 Continuous dual space of E 194 Continuous Mapping Derivative 3 Convex Function Set 182 Counterexample to Levi space, Non Locally convex space 242 Criterion for continuity 40 Curvilinear integral of Maps of Vector-Valued functions 160 Decreasing, Approximation numbers Sequence 19 Degree of Polynomials, Degree theory Degree of maps 124 Derivative, Directional, Gateaux 111 Differential, pq-Differential, Quasi-Differential (Bayoumi-Differential) 77 Dineen 14 Domain, Pseudoconvex of Holomorphy 228 Domain, Rienhardt, Logarithmically convex 72 Entire function, Continuous and Gateaux analytic 229 Equicontinuous Maps, Family Group 63 Equivalence relation, Vector space of maps of Quasi-tangency 78 Examples, Non Metrizable space, F-spaces 18 Extension Property Problem 7 Extension Theorem in Lbs and Lps in t.v.s. 11 Fixed points theorem of Brouwer or of Kakutanis Generalized 63 Frechet spaces, Product of Complete metric spaces 205 Function, Regular Bounded 158 Functional Analysis on p-Normed space 1 Fundamental Theorem of Calculus Riemann Integration Step functions 157 Fundamental Theorems in Functional Analysis 1 Hahn-Banach Extension property (HBEP), Separation property (HBSP) 7 Hardy space, Banach envelope of, Closed subspace of 259 Hausdorff Lps 255 Hoermander 72 Holomorphic extension problem, Dense subspaces, Closed subspace 221 Holomorphic functions, Three different classes of 196 Holomorphic Gateaux Analytic and continuous Quasi 124 Holomorphic mappings, Fixed points of, non convex domins in 63 Holomorphically complete Spaces Example of 217 Homeomorphism between Lbs 22 Homotopy, Continuous maps, Invariant 167 Image of separable Banach spaces 202 Inductive space, Locally p-convex space, Locally pseudoconvex spaces 257 Infinite dimensional, Complex analysis, Discussion on 224 Infinite dimensional, Holomorphy case 1 Infinitely, Quasi-differentials, Continuousely 152 Integral domain of Quasi-Analytic maps 155 Integral, Mean-Value theorem on Arc segment 176 Internal point of Arc segment of p-Extreme set 52 Inverse mapping theorem of Quasi-differentiable map 85 Isometry, Natural Isomorphic 34 Josefson Counterexample to Levi problem 228 Josefson Limited sets 212 K-space, Three-space problem 11 Kakutani, Fixed point theorem, Generalized 66 Kalton 14 Kalton Theorem, Failure of linear extension 10 Kisleman Approach Radius of convergence 239 Krein — Milman Theorem p-Convex hull of p-Extreme points 68 Lemma, Approximation Schwartz 96 Lemma, Zorn, Aurbach 10 Levi problem and Surjective Limit Approach in Lps 257 Levi problem in Metrizable spaces in Locally pseudoconvex spaces 247 Levi problem in PB-spaces (Bayoumi spaces) in F-space 241 Levi problem in Separable p-Banch spaces and Quotient Mapping Approach 258 Levi problem, Grumman and Kisleman Approach 243 Levi problem, Radius of convergence Approach Bayoumi PB-spaces 242 Linear Mapping Functional 2 Linear Mapping Space 1 8 Lipschitzian property, Generalized 80 Local Property, Constant map 153 Locally bounded Space, F-space 2 Locally Bounded space, Pseudoconvex space 8 m Quasi-differential 107 m-Expansion of maps, Finite Uniquness of 125 m-Linear map, 2-Linear map (Bilinear), Contiuous ... 30 m-Quasi tangency, m-quasi differential 124 Mapping into Product spaces, Quasi-differentiable 82 Martin’s theorem of p-Normed spaces 41 Mathematical Programming Nonlinear, Constraints 61 Mean-Value General Theorem of Integral 131 Mean-Value theorem, Lagrange, Real or Complex 90 Metric space, Translation invariant, Complete 229 Metric, Non decreasing by F-norm 246 Milman Generalized theorem of p-Extreme points 50 Multilinear maps of p-Banach space Continuous 29 Multinomial Formula Binomial Formula 36 Natural domin of Existance, Levi space 230 Normalized sequence of disjoint supports 223 Open mapping theorem of Locally bounded space 20 p-Convex combination p-Convex hull of Compact set 58 p-Convex hull, Absolutely 208 p-Convex set, Absolutely 51 p-Extreme Points sets 50 p-homogeneous, norm, quasi-norm Polynomial 24 Path of type Arc segment in 160 PB-property, Pseudoconvex boundery distance, PB-Space (Bayoumi Space) 231 Pelczynski theorem, Frechet space with b.a.p., Complemented L.c.s. with basis 244 Permutation 35 Physics, Thermodynamics, Application 8 Plurisubharmonic Functions, Logarithmically... metric 230 Point-wise Separation property 16 Polarization Formula of Symmetric m-Linear maps 38 Polynomially convex of Ball of Set 181 Polynomials, m-Homogenuous, Continuous 35 Power series, Properties between p-Normed spaces 136 Power series, Uniqueness of, Quasi-differential of 146 Principle of uniform boundedness Equicontinuous family Bounded pointwise 25 Product of p-Normed spaces, Cartesian 29 Properties of Bounding and Weakly bounding, Compact linear maps 206 Properties, Radius of convergence, Radius of boundedness 234 Property (p), Extension property, Separation property 11 Property, Finite intersection, PB-property 70 q-Banach Space, Separable 5 q-normed space 5 Quasi tangent, pq-Tangent of Two maps 78 Quasi-Analytic Continuation, Strong form, Weak form 153 Quasi-Analytic Principle of, Maps 151 Quasi-differential (or Bayoumi differential) of Multilinear maps of Polynomials 83 Quasi-Differential Higher, Gateaux 106 Quasi-Differential norm 2 Quasi-differential Properties of, Bayoumi 79 Quasi-Differential Second, Higher 101 Quasi-Holomorphic (or Bayoumi Holomorphic) Maps, Function 123 Quotient space, Quotient map, Complemented space 185 Radius of Absolute Convergence, Normal Convergence 144 Radius of convergence, Radius of boundedness of Holomorphic function 229 Relationship between Bayoumi and Frechet differentials, Bayoumi (Quasi) and Gateaux differentials 115 Relatively compact, sequentially compact 185 Riemann domain, Spread over Metric vector spaces 260 Rolewicz 183 Rolewicz Metric Linear Spaces 2 Schauder Basis Decomposition 185 Schwartz Symmetric theorem, Generalized 103 Separable Banach spaces, Levi Problem in some Separable p-Banach spaces 258 Separation Property Problem 7 Separation Theorem in Lbs (Locally bounded sp.) in Lps (Locally pseudoconvex sp.) 12 Sequence spaces with Logarithmically convex balls, with p-Convex ball 73 Space of Continuous linear maps L(E,F) of Continuous Polynomials P(E,F) 4 Space of Convex type, Sequence 73 Space, Locally p-convex Locally pseudoconvex (Lpc) 52 Space, Orlicz Montel or Schwartz 68 Sublinear Functional, Absolutely 8 Surjective limit of Lps, Preservation of Pseudonorm Surjective representation 254 Taylor formula with Lagrange Remainder with Assymptotic property 133 Taylor Polynomial Differentiation of Taylor formula 129 Theorem Generalized Milman 56 Theorems Hahn — Banach Mean value 8 Topology on L(E,F), Compact open... on H(U) 5 Uniform Convergence, Normal Convergence, Absolute Convergence 138 Universal constant of m-Linear map and Polynomial, Generalized 42 Vector spaces, Hahn — Banach Theorem in, Sublinear functional in 8 Vector sum of Bounding sets, Weakly bounding (or Limited) set 207 Weakly bounded sets, Bounded weakly-bounding sets Bounded sets 210 Weakly Bounding Closed 16 Weakly bounding sets in Lbs, Weakly bounding sets in F-spaces Limited sets in Lbs and F-spaces 192
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