Bayoumi A. — Foundations of Complex Analysis in Non Locally Convex Spaces: Function Theory without Convexity Condition :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Bayoumi A. — Foundations of Complex Analysis in Non Locally Convex Spaces: Function Theory without Convexity Condition

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Foundations of Complex Analysis in Non Locally Convex Spaces: Function Theory without Convexity Condition

Автор: 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.

The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 287

Добавлена в каталог: 10.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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 $\mathbb{C}^{n}$       63
Holomorphically complete Spaces Example of      217
Homeomorphism between Lbs      22
Homotopy, Continuous maps, Invariant      167
Image of separable Banach spaces $(l_{o})$ , Image of separable p-Banach spaces $(l_{p})$       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 ... $L(^{m}E,F)$       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 $\mathbb{C}$       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

О проекте