抽象调和分析 第1卷 第2版PDF电子书下载

Chapter One：Preliminaries 1

Section 1．Notation and terminology 1

Section 2．Group theory 3

Section 3．Topology 9

Chapter Two：Elements of the theory of topological groups 15

Section 4．Basic definitions and facts 16

Section 5．Subgroups and quotient groups 32

Section 6．Product groups and projective limits 52

Section 7．Properties of topological groups involving connectedness 60

Section 8．Invariant pseudo-metrics and separation axioms 67

Section 9．Structure theory for compact and locally compact Abelian groups 83

Section 10．Some special locally compact Abelian groups 106

Chapter Three：Integration on locally compact spaces 117

Section 11．Extension of a linear functional and construction of a measure 118

Section 12．The spaces ？p（X）（1？p？∞） 135

Section 13．Integration on product spaces 150

Section 14．Complex measures 166

Chapter Four：Invariant functionals 184

Section 15．The Haar integral 184

Section 16．More about Haar measure 215

Section 17．Invariant means defined for all bounded functions 230

Section 18．Invariant means on almost periodic functions 245

Chapter Five：Convolutions and group representations 261

Section 19．Introduction to convolutions 262

Section 20．Convolutions of functions and measures 283

Section 21．Introduction to representation theory 311

Section 22．Unitary representations of locally compact groups 335

Chapter Six：Characters and duality of locally compact Abelian groups 355

Section 23．The character group of a locally compact Abelian group 355

Section 24．The duality theorem 376

Section 25．Special structure theorems 399

Section 26．Miscellaneous consequences of the duality theorem 426

Appendix A：Abelian groups 439

B：Topological linear spaces 451

C：Introduction to normed algebras 469

Bibliography 492

Index of symbols 506

Index of authors and terms 509