INTEGRAL AND FUNCTIONAL ANALYSIS (UPDATED EDITION)
| Main Author: | |
|---|---|
| Format: | Electronic Book |
| Language: | English |
| Published: |
[S.l.] :
NOVA SCIENCE,
2021
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| Series: | Mathematics Research Developments Ser
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| Subjects: |
Table of Contents:
- Intro
- INTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION)
- INTEGRAL AND FUNCTIONALANALYSIS(UPDATED EDITION)
- Contents
- Preface
- Acknowledgments
- Chapter 1Preliminaries
- 1.1 Sets, Relations, Functions, Cardinals and Ordinals
- 1.2 Reals, Some Basic Theorems and Sequence Limits
- Problems
- Chapter 2Riemann 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
- Chapter 3Riemann-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 Situations
- Problems
- Chapter 4Lebesgue-Radon-StieltjesIntegrals
- 4.1 Foundational Material
- 4.2 Essential Properties
- 4.3 Convergence Theorems
- 4.4 Extension via Measurability
- 4.5 Double, Iterated and Generic Integrals
- Problems
- Chapter 5Absolute Continuitiesin Lebesgue Integrals
- 5.1 Lebesgue's Outer Measure and Vitali's Covering
- 5.2 Derivatives of Increasing Functions
- 5.3 Absolutely Continuous Functions
- 5.4 Cantor's Ternary Set and Singular Function
- 5.5 Lebesgue's Points
- Problems
- Chapter 6Metric Spaces
- 6.1 Metrizable Topology and Connectedness
- 6.2 Completeness
- 6.3 Compactness, Density and Separability
- Problems
- Chapter 7Continuous Mappings
- 7.1 Criteria for Continuity
- 7.2 Continuous Mappings over Compactor ConnectedMetric Spaces
- 7.3 Sequences of Mappings
- 7.4 Contractions
- 7.5 Structures of Metric Spaces
- Problems
- Chapter 8Normed Linear Spaces
- 8.1 Linear Spaces, Norms and Quotient Spaces
- 8.2 Finite Dimensional Spaces
- 8.3 Bounded Linear Operators
- 8.4 Linear Functionals via Hahn-Banach Extension
- Problems
- Chapter 9Banach Spaces via Operatorsand Functionals
- 9.1 Definition and Beginning Examples
- 9.2 Uniform Boundedness
- Open Map
- Closed Graph
- 9.3 Dual Banach Spaces by Examples
- 9.4 Weak and Weak* Topologies
- 9.5 Compact and Dual Operators
- Problems
- Chapter 10Hilbert Spaces and TheirOperators
- 10.1 Definition, Examples and Basic Properties
- 10.2 Orthogonality, Orthogonal Complementand Duality
- 10.3 Orthonormal Sets and Bases
- 10.4 Five Special Bounded Operators
- 10.5 Compact Operators via Spectrum
- Problems
- Hints or Solutions
- 1 Preliminaries
- 3 Riemann-Stieltjes Integrals
- 4 Lebesgue-Radon-Stieltjes Integrals
- 5 Absolute Continuities in Lebesgue Integrals
- 6 Metric Spaces
- 7 Continuous Mappings
- 8 Normed Linear Spaces
- 9 Banach Spaces via Operators and Functionals
- 10 Hilbert Spaces and Their Operators
- 2 Riemann Integrals
- References
- About the Author
- Index
- Blank Page
- Blank Page