抽象调和分析 第1卷 第2版

PrefacesChapter One: PreliminariesSection  1. Notation and terminologySection  2. Group theorySection  3. TopologyChapter Two: Elements of the theory of topological groupsSection 4. Basic definitions and factsSection  5. Subgroups and quotient groupsSection  6. Product groups arid projective limitsSection  7. Properties of topological groups involving connectednessSection  8. Invariant pseudo-metrics and separation axiomsSection 9. Structure theory for compact and locally compact AbeliangroupsSection 10. Some special locally compact Abel/an groupsChapter Three: Integration on locally compact spacesSection 11. Extension of a linear functional and construction of a measureSection 12. The spacesSection 13. Integration on product spacesSection 14. Complex measuresChapter Four: Invariant functionalsSection 15. The Haar integral  .Section 16. More about Haar measureSection 17. Invariant means defined for all bounded functionsSection |8. Invariant means on almost periodic functionsChapter Five: Convolutions and group representationsSection t9. Introduction to convolutionsSection 20. Convolutions of functions and measuresSection 2|. Introduction to representation theorySection 22. Unitary representations of locally compact groupsChapter Six: Characters and duality of locally compact Abelian groupsSection 23. The character group of a locally compact Abelian groupSection 24. The duality theoremSection 25. Special structure theoremsSection 26. Miscellaneous consequences of the duality theoremAppendix A: Abelian groupsB: Topological linear spacesC:  Introduction to normed algebrasBibliographyIndex of symbolsIndex of authors and terms