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Introductory Functional Analysis With Applications by Erwin Kreyszig


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INTRODUCTORY FUNCTIONAL ANALYSIS WITH APPLICATIONS written by Erwin Kreyszig . This is an other book of mathematics cover the following topics.

  • Metric Spaces
    Metric Space, Further Examples of Metric Spaces, Open Set, Closed Set, Neighborhood, Convergence, Cauchy Sequence, Completeness, Examples. Completeness Proofs, Completion of Metric Spaces

  • Normed Spaces. Banach Spaces
    Vector Space, Normed Space. Banach Space, Further Properties of Normed Spaces, Finite Dimensional Normed Spaces and Subspaces, Compactness and Finite Dimension, Linear Operators, Bounded and Continuous Linear Operators, Linear Functionals, Linear Operators and Functionals on Finite Dimensional Spaces, Normed Spaces of Operators. Dual Space

  • Inner Product Spaces. Hilbert Spaces
    Inner Product Space. Hilbert Space, Further Properties of Inner Product Spaces, Orthogonal Complements and Direct Sums, Orthonormal Sets and Sequences, Series Related to Orthonormal Sequences and Sets, Total Orthonormal Sets and Sequences, Legendre, Hermite and Laguerre Polynomials, Representation of Functionals on Hilbert Spaces, Hilbert-Adjoint Operator, Self-Adjoint, Unitary and Normal Operators

  • Fundamental Theorems for Normed and Banach Spaces
    Zorn's Lemma, Hahn-Banach Theorem, Hahn-Banach Theorem for Complex Vector Spaces and Normed Spaces, Application to Bounded Linear ~unctionals on C[a, b], Adjoint Operator, Reflexive Spaces, Category Theorem. Uniform Boundedness Theorem, Strong and Weak Convergence, Convergence of Sequences of Operators and Functionals, Application to Summability of Sequences, Numerical Integration and Weak* Convergence, Open Mapping Theorem, Closed Linear Operators. Closed Graph Theorem

  • Further Applications: Banach Fixed Point Theorem
    Banach Fixed Point Theorem, Application of Banach's Theorem to Linear Equations, Applications of Banach's Theorem to Differential, Equations, Application of Banach's Theorem to Integral, Equations

  • Further Applications: Approximation Theory
    Approximation in Normed Spaces, Uniqueness, Strict Convexity, Uniform Approximation, Chebyshev Polynomials, Approximation in Hilbert Space, Splines

  • Spectral Theory of Linear Operators in Normed, Spaces
    Spectral Theory in Finite Dimensional Normed Spaces, Basic Concepts, Spectral Properties of Bounded Linear Operators, Further Properties of Resolvent and Spectrum, Use of Complex Analysis in Spectral Theory, Banach Algebras, Further Properties of Banach Algebras

  • Compact Linear Operators on Normed Spaces and Their Spectrum.
    Compact Linear Operators on Normed Spaces, Further Properties of Compact Linear Operators, Spectral Properties of Compact Linear Operators on Normed Spaces, Further Spectral Properties of Compact Linear Operators, Operator Equations Involving Compact Linear Operators, Further Theorems of Fredholm Type, Fredholm Alternative

  • Spectral Theory of Bounded Self-Adjoint Linear Operators
    Spectral Properties of Bounded Self-Adjoint Linear Operators, Further Spectral Properties of Bounded Self-Adjoint Linear Operators, Positive Operators, square Roots of a Positive Operator, Projection Operators, Further Properties of Projections, Spectral Family, Spectral Family of a Bounded Self-Adjoint Linear Operator, Spectral Representation of Bounded Self-Adjoint Linear Operators, Extension of the Spectral Theorem to Continuous Functions, Properties of the Spectral Family of a Bounded SelfAd,ioint Linear Operator

  • Unbounded Linear Operators in Hilbert Space
    Unbounded Linear Operators and their Hilbert-Adjoint Operators, Hilbert-Adjoint Operators, Symmetric and Self-Adjoint Linear Operators, Closed Linear Operators and Cldsures, Spectral Properties of Self-Adjoint Linear Operators, Spectral Representation of Unitary Operators, Spectral Representation of Self-Adjoint Linear Operators, Multiplication Operator and Differentiation Operator

  • Unbounded Linear Operators in Quantum Mechanics
    Basic Ideas. States, Observables, Position Operator, Momentum Operator. Heisenberg Uncertainty Principle, Time-Independent Schrodinger Equation, Hamilton Operator, Time-Dependent Schrodinger Equation

  • Appendix 1. Some Material for Review and Reference
    Sets, Mappings, Families, Equivalence Relations, Compactness, Supremum and Infimum, Cauchy Convergence Criterion, Groups

  • Appendix 2. Answers to Odd-Numbered Problems.
  • Appendix 3. References.

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