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Functional Analysis: An Elementary Introduction
About this Title
Markus Haase, Delft University of Technology, Delft, The Netherlands
Publication: Graduate Studies in Mathematics
Publication Year:
2014; Volume 156
ISBNs: 978-0-8218-9171-1 (print); 978-1-4704-1858-8 (online)
DOI: https://doi.org/10.1090/gsm/156
MathSciNet review: MR3237610
MSC: Primary 46-01
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Inner product spaces
- Chapter 2. Normed spaces
- Chapter 3. Distance and approximation
- Chapter 4. Continuity and compactness
- Chapter 5. Banach spaces
- Chapter 6. The contraction principle
- Chapter 7. The Lebesgue spaces
- Chapter 8. Hilbert space fundamentals
- Chapter 9. Approximation theory and Fourier analysis
- Chapter 10. Sobolev spaces and the Poisson problem
- Chapter 11. Operator theory I
- Chapter 12. Operator theory II
- Chapter 13. Spectral theory of compact self-adjoint operators
- Chapter 14. Applications of the spectral theorem
- Chapter 15. Baire’s theorem and its consequences
- Chapter 16. Duality and the Hahn-Banach theorem
- Historical remarks
- Appendix A. Background
- Appendix B. The completion of a metric space
- Appendix C. Bernstein’s proof of Weierstrass’ theorem
- Appendix D. Smooth cutoff functions
- Appendix E. Some topics from Fourier analysis
- Appendix F. General orthonormal systems
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