Introductory Functional Analysis With Applications,9780471504597

Introductory Functional Analysis With Applications

by
Edition: 1st
ISBN13: 9780471504597
ISBN10: 0471504599
Format: Paperback
Pub. Date: 1991-01-16
Publisher(s): Wiley
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Summary

Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.

Author Biography

Erwin O. Kreyszig was a German Canadian applied mathematician and the Professor of Mathematics at Carleton University in Ottawa, Ontario, Canada. He was a pioneer in the field of applied mathematics: non-wave replicating linear systems.

Table of Contents

Metric Spaces
1(49)
Metric Space
2(7)
Further Examples of Metric Spaces
9(8)
Open Set, Closed Set, Neighborhood
17(8)
Convergence, Cauchy Sequence, Completeness
25(7)
Examples. Completeness Proofs
32(9)
Completion of Metric Spaces
41(8)
Normed Spaces. Banach Spaces
49(78)
Vector Space
50(8)
Normed Space. Banach Space
58(9)
Further Properties of Normed Spaces
67(5)
Finite Dimensional Normed Spaces and Subspaces
72(5)
Compactness and Finite Dimension
77(5)
Linear Operators
82(9)
Bounded and Continuous Linear Operators
91(12)
Linear Functionals
103(8)
Linear Operators and Functionals on Finite Dimensional Spaces
111(6)
Normed Spaces of Operators. Dual Space
117(10)
Inner Product Spaces. Hilbert Spaces
127(82)
Inner Product Space. Hilbert Space
128(8)
Further Properties of Inner Product Spaces
136(6)
Orthogonal Complements and Direct Sums
142(9)
Orthonormal Sets and Sequences
151(9)
Series Related to Orthonormal Sequences and Sets
160(7)
Total Orthonormal Sets and Sequences
167(8)
Legendre, Hermite and Laguerre Polynomials
175(13)
Representation of Functionals on Hilbert Spaces
188(7)
Hilbert-Adjoint Operator
195(6)
Self-Adjoint, Unitary and Normal Operators
201(8)
Fundamental Theorems for Normed and Banach Spaces
209(90)
Zorn's Lemma
210(3)
Hahn-Banach Theorem
213(5)
Hahn-Banach Theorem for Complex Vector Spaces and Normed Spaces
218(7)
Application to Bounded Linear Functionals on C[a, b]
225(6)
Adjoint Operator
231(8)
Reflexive Spaces
239(7)
Category Theorem. Uniform Boundedness Theorem
246(10)
Strong and Weak Convergence
256(7)
Convergence of Sequences of Operators and Functionals
263(6)
Application to Summability of Sequences
269(7)
Numerical Integration and Weak* Convergence
276(9)
Open Mapping Theorem
285(6)
Closed Linear Operators. Closed Graph Theorem
291(8)
Further Applications: Banach Fixed Point Theorem
299(28)
Banach Fixed Point Theorem
299(8)
Application of Banach's Theorem to Linear Equations
307(7)
Applications of Banach's Theorem to Differential Equations
314(5)
Application of Banach's Theorem to Integral Equations
319(8)
Further Applications: Approximation Theory
327(36)
Approximation in Normed Spaces
327(3)
Uniqueness, Strict Convexity
330(6)
Uniform Approximation
336(9)
Chebyshev Polynomials
345(7)
Approximation in Hilbert Space
352(4)
Splines
356(7)
Spectral Theory of Linear Operators in Normed Spaces
363(42)
Spectral Theory in Finite Dimensional Normed Spaces
364(6)
Basic Concepts
370(4)
Spectral Properties of Bounded Linear Operators
374(5)
Further Properties of Resolvent and Spectrum
379(7)
Use of Complex Analysis in Spectral Theory
386(8)
Banach Algebras
394(4)
Further Properties of Banach Algebras
398(7)
Compact Linear Operators on Normed Spaces and Their Spectrum
405(54)
Compact Linear Operators on Normed Spaces
405(7)
Further Properties of Compact Linear Operators
412(7)
Spectral Properties of Compact Linear Operators on Normed Spaces
419(9)
Further Spectral Properties of Compact Linear Operators
428(8)
Operator Equations Involving Compact Linear Operators
436(6)
Further Theorems of Fredholm Type
442(9)
Fredholm Alternative
451(8)
Spectral Theory of Bounded Self-Adjoint Linear Operators
459(64)
Spectral Properties of Bounded Self-Adjoint Linear Operators
460(5)
Further Spectral Properties of Bounded Self-Adjoint Linear Operators
465(4)
Positive Operators
469(7)
Square Roots of a Positive Operator
476(4)
Projection Operators
480(6)
Further Properties of Projections
486(6)
Spectral Family
492(5)
Spectral Family of a Bounded Self-Adjoint Linear Operators
497(8)
Spectral Representation of Bounded Self-Adjoint Linear Operators
505(7)
Extension of the Spectral Theorem to Continuous Functions
512(4)
Properties of the Spectral Family of a Bounded Self-Adjoint Linear Operator
516(7)
Unbounded Linear Operators in Hilbert Space
523(48)
Unbounded Linear Operators and their Hilbert-Adjoint Operators
524(6)
Hilbert-Adjoint Operators, Symmetric and Self-Adjoint Linear Operators
530(5)
Closed Linear Operators and Closures
535(6)
Spectral Properties of Self-Adjoint Linear Operators
541(5)
Spectral Representation of Unitary Operators
546(10)
Spectral Representation of Self-Adjoint Linear Operators
556(6)
Multiplication Operator and Differentiation Operator
562(9)
Unbounded Linear Operators in Quantum Mechanics
571(38)
Basic Ideas. States, Observables, Position Operator
572(4)
Momentum Operator. Heisenberg Uncertainty Principle
576(7)
Time-Independent Schrodinger Equation
583(7)
Hamilton Operator
590(8)
Time-Dependent Schrodinger Equation
598(11)
Appendix 1. Some Material for Review and Reference 609(14)
A1.1 Sets
609(4)
A1.2 Mappings
613(4)
A1.3 Families
617(1)
A1.4 Equivalence Relations
618(1)
A1.5 Compactness
618(1)
A1.6 Supremum and Infimum
619(1)
A1.7 Cauchy Convergence Criterion
620(2)
A1.8 Groups
622(1)
Appendix 2. Answers to Odd-Numbered Problems 623(52)
Appendix 3. References 675(6)
Index 681

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