Introduction to Abstract Harmonic Analysis

This classic monograph is the work of a prominent contributor to the field of harmonic analysis. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. Prerequisites include a knowledge of the concepts of elementary modern algebra and of metric space topology.
The first three chapters feature concise, self-contained treatments of measure theory, general topology, and Banach space theory that will assist students in their grasp of subsequent material. An in-depth exposition of Banach algebra follows, along with examinations of the Haar integral and the deduction of the standard theory of harmonic analysis on locally compact Abelian groups and compact groups. Additional topics include positive definite functions and the generalized Plancherel theorem, the Wiener Tauberian theorem and the Pontriagin duality theorem, representation theory, and the theory of almost periodic functions.

1101380573
Introduction to Abstract Harmonic Analysis

This classic monograph is the work of a prominent contributor to the field of harmonic analysis. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. Prerequisites include a knowledge of the concepts of elementary modern algebra and of metric space topology.
The first three chapters feature concise, self-contained treatments of measure theory, general topology, and Banach space theory that will assist students in their grasp of subsequent material. An in-depth exposition of Banach algebra follows, along with examinations of the Haar integral and the deduction of the standard theory of harmonic analysis on locally compact Abelian groups and compact groups. Additional topics include positive definite functions and the generalized Plancherel theorem, the Wiener Tauberian theorem and the Pontriagin duality theorem, representation theory, and the theory of almost periodic functions.

19.95 In Stock
Introduction to Abstract Harmonic Analysis

Introduction to Abstract Harmonic Analysis

by Lynn H. Loomis
Introduction to Abstract Harmonic Analysis

Introduction to Abstract Harmonic Analysis

by Lynn H. Loomis

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$19.95 
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Overview

This classic monograph is the work of a prominent contributor to the field of harmonic analysis. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. Prerequisites include a knowledge of the concepts of elementary modern algebra and of metric space topology.
The first three chapters feature concise, self-contained treatments of measure theory, general topology, and Banach space theory that will assist students in their grasp of subsequent material. An in-depth exposition of Banach algebra follows, along with examinations of the Haar integral and the deduction of the standard theory of harmonic analysis on locally compact Abelian groups and compact groups. Additional topics include positive definite functions and the generalized Plancherel theorem, the Wiener Tauberian theorem and the Pontriagin duality theorem, representation theory, and the theory of almost periodic functions.


Product Details

ISBN-13: 9780486481234
Publisher: Dover Publications
Publication date: 07/19/2011
Series: Dover Books on Mathematics Series
Pages: 208
Product dimensions: 5.40(w) x 8.50(h) x 0.50(d)

Table of Contents

Chapter I Topology

1 Sets 1

2 Topology 3

3 Separation axioms and theorems 5

4 The Stone-Weierstrass theorem 8

5 Cartesian products and weak topology 10

Chapter II Banach Spaces

6 Normed linear spaces 13

7 Bounded linear transformations 15

8 Linear functionals 18

9 The weak topology for X* 22

10 Hilbert space 23

11 Involution on B(H) 27

Chapter III Integration

12 The Daniell integral 29

13 Equivalence and measurability 34

14 The real Lp-spaces 37

15 The conjugate space of Lp 40

16 Integration on locally compact Hausdorff spaces 43

17 The complex Lp-spaces 46

Chapter IV Banach Algebras

18 Definition and examples 48

19 Function algebras 50

20 Maximal ideals 58

21 Spectrum; adverse 63

22 Banach algebras; elementary theory 66

23 The maximal ideal space of a commutative Banach algebra 69

24 Some basic general theorems 75

Chapter V Some Special Banach Algebras

25 Regular commutative Banach algebras 82

26 Banach algebras with involutions 87

27 H*-algebras 100

Chapter VI The Haar Integral

28 The topology of locally compact groups 108

29 The Haar integral 112

30 The modular function 117

31 The group algebra 120

32 Representations 127

33 Quotient measures 130

Chapter VII Locally Compact Abelian Groups

34 The character group 134

35 Examples 138

36 The Bochner and Plancherel theorems 141

37 Miscellaneous theorems 147

38 Compact Abelian groups and generalized Fourier series 153

Chapter VIII Compact Groups and Almost Periodic Functions

39 The group algebra of a compact group 156

40 Representation theory 161

41 Almost periodic functions 165

Chapter IX Some Further Developments

42 Non-commutative theory 174

43 Commutative theory 179

Bibliography 185

Index 188

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