Introductory Functional Analysis With ~ Applications by Kreyszig || Download PDF

 Introductory Functional Analysis With ~ Applications

Introductory Functional Analysis With ~ Applications by Kreyszig || Download PDF

If you're are searching Introductory Functional Analysis with Applications then, you're in the right place. There you can download a functional analysis book for study purposes. This book is useful for most of this university & includes in the compulsory syllabus, So, it's necessary for every student. This also has very informative materials for knowledge purposes, So read this functional analysis book carefully. The book is suitable for a one-semester course meeting five hours per week or for a two-semester course meeting three hours per week.

Course Contents:

  • Chapter 1. Metric Spaces . . . .2
  • 1.1 Metric Space 2
  • 1.2 Further Examples of Metric Spaces 9
  • 1.3 Open Set, Closed Set, Neighborhood 17
  • 1.4 Convergence, Cauchy Sequence, Completeness 25
  • 1.5 Examples. Completeness Proofs 32
  • 1.6 Completion of Metric Spaces 41
  • Chapter 2. Normed Spaces. Banach Spaces. . . . . 49
  • 2.1 Vector Space 50
  • 2.2 Normed Space. Banach Space 58
  • 2.3 Further Properties of Normed Spaces 67
  • 2.4 Finite Dimensional Normed Spaces and Subspaces 72
  • 2.5 Compactness and Finite Dimension 77
  • 2.6 Linear Operators 82
  • 2.7 Bounded and Continuous Linear Operators 91
  • 2.8 Linear Functionals 103
  • 2.9 Linear Operators and Functionals on Finite-Dimensional Spaces 111
  • 2.10 Normed Spaces of Operators. Dual Space 117
  • Chapter 3. Inner Product Spaces. Hilbert Spaces. . .127
  • 3.1 Inner Product Space. Hilbert Space 128
  • 3.2 Further Properties of Inner Product Spaces 136
  • 3.3 Orthogonal Complements and Direct Sums 142
  • 3.4 Orthonormal Sets and Sequences 151
  • 3.5 Series Related to Orthonormal Sequences and Sets 160
  • 3.6 Total Orthonormal Sets and Sequences 167
  • 3.7 Legendre, Hermite and Laguerre Polynomials 175
  • 3.8 Representation of Functionals on Hilbert Spaces 188
  • 3.9 Hilbert-Adjoint Operator 195
  • 3.10 Self-Adjoint, Unitary and Normal Operators 201
  • Chapter 4. Fundamental Theorems for Normed and Banach Spaces. . . . . . . . . . . 209
  • 4.1 Zorn's Lemma 210
  • 4.2 Hahn-Banach Theorem 213
  • 4.3 Hahn-Banach Theorem for Complex Vector Spaces and Normed Spaces 218
  • 4.4 Application to Bounded Linear ~unctionals on C[a, b] 225
  • 4.5 Adjoint Operator 231
  • 4.6 Reflexive Spaces 239
  • 4.7 Category Theorem. Uniform Boundedness Theorem 246
  • 4.8 Strong and Weak Convergence 256
  • 4.9 Convergence of Sequences of Operators and Functionals 263
  • 4.10 Application to Summability of Sequences 269
  • 4.11 Numerical Integration and Weak* Convergence 276
  • 4.12 Open Mapping Theorem 285
  • 4.13 Closed Linear Operators. Closed Graph Theorem 291
  • Chapter 5. Further Applications: Banach Fixed Point Theorem . . . . . . . . . . . . 299
  • 5.1 Banach Fixed Point Theorem 299
  • 5.2 Application of Banach's Theorem to Linear Equations 307
  • 5.3 Applications of Banach's Theorem to Differential Equations 314
  • 5.4 Application of Banach's Theorem to Integral Equations 319
  • Chapter 6. Further Applications: ApproximationTheory ..... . . . . . . . 327
  • 6.1 Approximation in Normed Spaces 327
  • 6.2 Uniqueness, Strict Convexity 330
  • 6.3 Uniform Approximation 336
  • 6.4 Chebyshev Polynomials 345
  • 6.5 Approximation in Hilbert Space 352
  • 6.6 Splines 356
  • 7.3 Spectral Properties of Bounded Linear Operators 374
  • 7.4 Further Properties of Resolvent and Spectrum 379
  • 7.5 Use of Complex Analysis in Spectral Theory 386
  • 7.6 Banach Algebras 394
  • 7.7 Further Properties of Banach Algebras 398
  • Chapter 8. Compact Linear Operators on Normed Spaces and Their Spectrum...... 405
  • 8.1 Compact Linear Operators on Normed Spaces 405
  • 8.2 Further Properties of Compact Linear Operators 412
  • 8.3 Spectral Properties of Compact Linear Operators on Normed Spaces 419
  • 8.4 Further Spectral Properties of Compact Linear Operators 428
  • 8.5 Operator Equations Involving Compact Linear Operators 436
  • 8.6 Further Theorems of Fredholm Type 442
  • 8.7 Fredholm Alternative 451
  • Chapter 9. Spectral Theory of Bounded Self-Adjoint Linear Operators....... 459
  • 9.1 Spectral Properties of Bounded Self-Adjoint Linear Operators 460
  • 9.2 Further Spectral Properties of Bounded Self-Adjoint Linear Operators 465
  • 9.3 Positive Operators 469
  • 9.4 Square Roots of a Positive Operator 476
  • 9.5 Projection Operators 480
  • 9.6 Further Properties of Projections 486
  • 9.7 Spectral Family 492
  • 9.8 Spectral Family of a Bounded Self-Adjoint Linear Operator 497
  • 9.9 Spectral Representation of Bounded Self-Adjoint Linear Operators 505
  • 9.10 Extension of the Spectral Theorem to Continuous Functions 512
  • 9.11 Properties of the Spectral Family of a Bounded Self- Ad,joint Linear Operator 516
  • Chapter 10. Unbounded Linear Operators in Hilbert Space . . . . . . . . . . . . 523
  • 10.1 Unbounded Linear Operators and their Hilbert-Adjoint Operators 524
  • 10.2 Hilbert-Adjoint Operators, Symmetric and Self-Adjoint Linear Operators 530
  • 10.3 Closed Linear Operators and Cldsures 535
  • 10.4 Spectral Properties of Self-Adjoint Linear Operators 541
  • 10.5 Spectral Representation of Unitary Operators 546
  • 10.6 Spectral Representation of Self-Adjoint Linear Operators 556
  • 10.7 Multiplication Operator and Differentiation Operator 562
  • Chapter 11. Unbounded Linear Operators in Quantum Mechanics . . . . . . 571
  • 11.1 Basic Ideas. States, Observables, Position Operator 572
  • 11.2 Momentum Operator. Heisenberg Uncertainty Principle 576
  • 11.3 Time-Independent Schrodinger Equation 583
  • 11.4 Hamilton Operator 590
  • 11.5 Time-Dependent Schrodinger Equation 598

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