UID:
almahu_9949697518302882
Format:
1 online resource (305 p.)
Edition:
1st ed.
ISBN:
1-281-02950-5
,
9786611029500
,
0-08-053192-X
Series Statement:
North-Holland mathematics studies, v. 193
Content:
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 broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-c
Note:
Description based upon print version of record.
,
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
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5.1 MEAN-VALUE THEOREM IN REAL SPACES5.2 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
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CHAPTER 9. BOUNDING AND WEAKLY-BOUNDING SETS9.1 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
,
English
Additional Edition:
ISBN 0-444-50056-1
Language:
English
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