抽象调和分析-第1卷-第2版 本书特色

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.

抽象调和分析-第1卷-第2版 目录

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