A Course in Functional Analysis and Measure Theory
Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book...
Κύριος συγγραφέας: | |
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Συγγραφή απο Οργανισμό/Αρχή: | |
Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
Γλώσσα: | English |
Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2018.
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Έκδοση: | 1st ed. 2018. |
Σειρά: | Universitext,
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Θέματα: | |
Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Introduction
- Chapter 1. Metric and topological spaces
- Chapter 2. Measure theory
- Chapter 3. Measurable functions
- Chapter 4. The Lebesgue integral
- Chapter 5. Linear spaces, linear functionals, and the Hahn-Banach theorem
- Chapter 6. Normed spaces
- Chapter 7. Absolute continuity of measures and functions. Connection between derivative and integral
- Chapter 8. The integral on C(K)
- Chapter 9. Continuous linear functionals
- Chapter 10. Classical theorems on continuous operators
- Chapter 11. Elements of spectral theory of operators. Compact operators
- Chapter 12. Hilbert spaces
- Chapter 13. Functions of an operator
- Chapter 14. Operators in Lp
- Chapter 15. Fixed-point theorems and applications
- Chapter 16. Topological vector spaces
- Chapter 17. Elements of duality theory
- Chapter 18. The Krein-Milman theorem and applications
- References. Index.