Elementary Functional Analysis
eBook - PDF

Elementary Functional Analysis

  1. 192 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Elementary Functional Analysis

Book details
Table of contents
Citations

About This Book

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

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Yes, you can access Elementary Functional Analysis by Charles Swartz in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.

Information

Publisher
WSPC
Year
2009
ISBN
9789813107526
Topic
Mathematics
Subtopic
Functional Analysis
Index
Mathematics

Table of contents

  1. Contents
  2. Preface
  3. 1. Normed Linear and Banach Spaces
  4. 2. Linear Operators
  5. 3. Quotient Spaces
  6. 4. Finite Dimensional Normed Spaces
  7. 5. Inner Product and Hilbert Spaces
  8. 6. The Hahn-Banach Theorem
  9. 7. Applications of the Hahn-Banach Theorem to Normed Spaces
  10. 8. The Uniform Boundedness Principle
  11. 9. Weak Convergence
  12. 10. The Open Mapping and Closed Graph Theorems
  13. 11. Projections
  14. 12. Schauder Basis
  15. 13. Transpose and Adjoints of Continuous Linear Operators
  16. 14. Compact Operators
  17. 15. The Fredholm Alternative
  18. 16. The Spectrum of an Operator
  19. 17. Subdivisions of the Spectrum
  20. 18. The Spectrum of a Compact Operator
  21. 19. Symmetric Linear Operators
  22. 20. The Spectral Theorem for Compact Symmetric Operators
  23. 21. Symmetric Operators with Compact Inverse
  24. 22. Bounded Self Adjoint Operators
  25. 23. Orthogonal Projections
  26. 24. Sesquilinear Functionals
  27. 25. The Spectral Theorem for Bounded Self Adjoint Operators
  28. 26. An Operational Calculus
  29. 27. The Spectral Theorem for Normal Operators
  30. Appendix A Functions of Bounded Variation
  31. Appendix B The Riemann-Stieltjes Integral
  32. Appendix C The Dual of C[a; b]
  33. Appendix D The Baire Category Theorem
  34. References
  35. Index