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Integral and Functional Analysis
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Authors: Jie Xiao (Dept. of Mathematics and Statistics, Memorial Univ. of Newfoundland, St. John's, Canada) 
Book Description:
This book 'Integral And Functional Analysis' is based on two closely-related courses:(a) Integration and Metric Spaces; (b) Functional Analysis, which have been offered over the past four years at Memorial University of Newfoundland (MUN). Though the contents of Functional Analysis have been used for both an undergraduate course and an introductory graduate course, this text is designed primarily for the undergraduate students. It is assumed that students have some familiarity with Introductory Calculus and Linear Algebra plus the basic (direct, indirect) proof methods.

Table of Contents:
Preface pp.i-x

Chapter 1 - Preliminaries; pp. 1-16
1.1 Sets, Relations, Functions, Cardinals and Ordinals
1.2 Reals, Some Basic Theorems and Sequence Limits

Chapter 2 - Riemann Integrals; pp. 17-44
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

Chapter 3 - Riemann-Stieltjes Integrals; pp. 45-68
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

Chapter 4 - Lebesgue-Radon-Stieltjes Integrals; pp. 69-108
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

Chapter 5 - Metric Spaces; pp. 109-128
5.1 Metrizable Topology
5.2 Completeness
5.3 Compactness, Density and Separability

Chapter 6 - Continuous Maps; pp. 129-148
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

Chapter 7 - Normed Linear Spaces; pp. 149-172
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

Chapter 8 - Banach Spaces via Operators and Functionals; pp. 173-204
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

Chapter 9 - Hilbert Spaces and Their Operators; pp. 205-238
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

Hints and Solutions pp.239-280

References pp.281-284

Index pp.285-287

   Binding: Hardcover
   Pub. Date: 2008
   Pages: 297
   ISBN: 1-60021-784-2
   Status: AV
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
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