抽象調和分析(第1卷·第2版)

抽象調和分析(第1卷·第2版)
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內容簡介

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 1962——1978， 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.
 

目錄

Prefaces

Chapter One: Preliminaries
Section 1. Notation and terminology
Section 2. Group theory
Section 3. Topology

Chapter 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 Abelian
groups
Section 10. Some special locally compact Abel/an groups

Chapter 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 measures

Chapter 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 functions

Chapter 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 groups

Chapter 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
Bibliography
Index of symbols
Index of authors and terms
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