抽象调和分析 第1卷 第2版

　　It has not been possible to rewrite the entire book for this Second Edition. It would have been gratifying to resurvey the theory of topo-logical groups in the light of progress made in the period t962–t978, to amplify some sections and curtail others, and in general to profit from our experience since the book was published. Market conditions and other commitments incurred by the authors have dictated otherwise. We have nonetheless taken advantage of the kindness of Springer-Verlag to make a number of improvements in the text and of course to correct misprints and mathematical blunders.

PrefacesChapter One: Preliminaries Section 1. Notation and terminology Section 2. Group theory Section 3. TopologyChapter Two: Elements of the theory of topological groups Section 4. Basic definitions and facts Section 5. Subgroups and quotient groups Section 6. Product groups arid projective limits Section 7. Properties of topological groups involving connectedness Section 8. Invariant pseudo-metrics and separation axioms Section 9. Structure theory for compact and locally compact Abeliangroups Section 10. Some special locally compact Abel/an groupsChapter Three: Integration on locally compact spaces Section 11. Extension of a linear functional and construction of a measure Section 12. The spaces Section 13. Integration on product spaces Section 14. Complex measuresChapter Four: Invariant functionals Section 15. The Haar integral . Section 16. More about Haar measure Section 17. Invariant means defined for all bounded functions Section |8. Invariant means on almost periodic functionsChapter Five: Convolutions and group representations Section t9. Introduction to convolutions Section 20. Convolutions of functions and measures Section 2|. Introduction to representation theory Section 22. Unitary representations of locally compact groupsChapter 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 theoremAppendix A: Abelian groupsB: Topological linear spacesC: Introduction to normed algebrasBibliographyIndex of symbolsIndex of authors and terms