抽象调和分析 第1卷（第2版 英文影印版）
出版时间：2014年版
丛编项： 经典数学丛书
内容简介
It has not been possible to rewrite the entire book for this Second Edition. It would have been gratifying to resurvey the theory of topological 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.
We are in debt to the readers who have written to us or spoken with us about the text， and we have tried to follow their suggestions. We are happy here to record our gratitude to ROBER-r B. BURCKEL， W. WISTAR COMFORT， ROBERT E. EDWARDS， ROBERT'E. JAMISON， JORGE M. L6PEZ， THEODORE W. PALMER， WILLARD A. PARKER， KARL R. STROMBERG， and FRED THOELE， as well as to a host of others who have kindly made suggestions to us.
目录
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 and projectivelimits
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 speciallocally compact Abelian groups
Chapter Three： Integration on locally compact spaces
Section 11. Extension of a linear functional and construction of a Jncasure
Section 12.Thespaces
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 18.Invariant means on almost periodic functions
Chapter 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 locallycompact 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
