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Integral and functional analysis

Author: Jie Xiao
Publisher: New York : Nova Science Publishers, ©2008.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jie Xiao
ISBN: 9781600217845 1600217842
OCLC Number: 145431824
Description: x, 287 pages ; 27 cm
Contents: Preface; 1. Preliminaries; 1.1. Sets, Relations, Functions, Cardinals and Ordinals; 1.2. Reals, Some Basic Theorems and Sequence Limits Problems; 2. Riemann Integrals; 2.1. Definitions, Examples, and Basic Properties; 2.2. Algebraic Operations and the Darboux Criterion; 2.3. Fundamental Theorem of Calculus; 2.4. Improper Integrals Problems; 3. Riemann-Stieltjes Integrals; 3.1. Functions of Bounded Variation; 3.2. Definition and Basic Properties; 3.3. Nonexistence and Existence for Integrals; 3.4. Evaluations of Integrals; 3.5. Improper Cases Problems; 4. Lebesgue-Radon-Stieltjes Integrals; 4.1. Foundational Material; 4.2. Essential Properties; 4.3. Convergence Theorems; 4.4. Extension via Measurability; 4.5. Double and Iterated Integrals with Applications Problems; 5. Metric Spaces; 5.1. Metrizable Topology; 5.2. Completeness; 5.3. Compactness, Density and Separability Problems; 6. Continuous Maps; 6.1. Criteria for Continuity; 6.2. Continuous Maps on Compact or Connected Spaces; 6.3. Sequences of Mappings; 6.4. Contractions; 6.5. Equivalence of Metric Spaces Problems; 7. Normed Linear Spaces; 7.1. Linear Spaces, Norms and Quotient Spaces; 7.2. Finite Dimensional Spaces; 7.3. Bounded Linear Operators; 7.4. Linear Functionals via Hahn-Banach Extension Problems; 8. Banach Spaces via Operators and Functionals; 8.1. Definition and Beginning Examples; 8.2. Uniform Boundedness, Open Map and Closed Graph; 8.3. Dual Banach Spaces by Examples; 8.4. Weak and Weak Topologies; 8.5. Compact and Dual Operators Problems; 9. Hilbert Spaces and Their Operators; 9.1. Definition, Examples and Basic Properties; 9.2. Orthogonality, Orthogonal Complement and Duality; 9.3. Orthonormal Sets and Bases; 9.4. Five Special Bounded Operators; 9.5. Compact Operators via the Spectrum; Problems; Hints and Solutions; References; Index.
Responsibility: Jie Xiao.
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