Abstract Harmonic Analysis

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. Language: English