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

Author: Aboubakr Bayoumi
Publisher: Amsterdam ; Boston : Elsevier, 2003.
Series: North-Holland mathematics studies, v. 193.
Edition/Format:   eBook : Document : English : 1st edView all editions and formats
Summary:
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 functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bayoumi, Aboubakr.
Foundations of complex analysis in non locally convex spaces.
Amsterdam ; Boston : Elsevier, 2003
(DLC) 2004272132
(OCoLC)53155238
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Aboubakr Bayoumi
ISBN: 9780444500564 0444500561 008053192X 9780080531922
OCLC Number: 162577991
Description: 1 online resource (xvi, 278 pages) : illustrations.
Contents: 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 FRIÉCHET 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.
Series Title: North-Holland mathematics studies, v. 193.
Responsibility: Aboubakr Bayoumi.
More information:

Abstract:

Covers the fundamental theorems in complex and functional analysis. This book includes generalized forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems,  Read more...

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"...this book is definitely a contribution to the subject..."Richard M. Aron, in: (Mathematical Reviews, 2004)

 
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