Abstract Harmonic Analysis

Inhaltsverzeichnis

• One: Preliminaries.
• Section 1. Notationand terminology.
• Section 2. Group theory.
• Section 3. Topology.
• ChapterTwo : Elementsof thetheoryof topological groups.
• Section 4. Basic definitions and facts.
• Section 5. Subgroups and quotient groups.
• Section 6. Product groups and projective limits.
• Section 7. Properties of topologicalgroups involving connectedness.
• Section 8. Invariant pseudo-metrics and separation axioms.
• Section 9. Structure theory for compact and locally compact Abelian groups.
• Section 10. Some special locally compact Abelian groups.
• Three: Integration on locally compact spaces.
• Section 11. Extension of a linear functional and construction of a measure.
• Section 12. The spaces Lp(X) (1 ? p ? ?).
• Section 13. Integration on product spaces.
• Section 14. Complex measures.
• Four: Invariant functionals.
• Section 15. The Haar integral.
• Section 16. More about Haar measure.
• Section 17. Invariant means defined for all bounded functions.
• Section 18. Invariant means on almost periodic functions.
• Five: Convolutions and group representations.
• Section 19. Introduction to convolutions.
• Section 20. Convolutions of functions and measures.
• Section 21. Introduction to representation theory.
• Section 22. Unitary representations of locally compact groups.
• Six : Characters and duality of locally compact Abelian groups.
• Section 23. The character group of a locally compact Abelian group.
• Section 24. The duality theorem.
• Section 25. Special structure theorems.
• Section 26. Miscellaneous consequences of the duality theorem.
• Appendix A: Abelian groups.
• B: Topological linear spaces.
• C: Introduction to normed algebras.
• Index of symbols.
• Index of authors and terms.