Elements of abstract harmonic analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1965
|
| Ausgabe: | 2. print. |
| Schriftenreihe: | Academic paperbacks : Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 250 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Elements of abstract harmonic analysis |c by George Bachman |
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Datensatz im Suchindex
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| adam_text | Contents
PREFACE V
SYMBOLS USED IN TEXT X
Chapter 1 The Fourier Transform on the Real Line for
Functions in L] 1
Introduction 1
Notation 1
The Fourier Transform 2
Recovery 4
Relation between the Norms of the Fourier Transform and the
Function 10
Appendix to Chapter 1 15
Exercises 17
References 18
Chapter 2 The Fourier Transform on the Real Line for
Functions in L2 19
Inversion in h% 21
Normed and Banach Algebras 25
Analytic Properties of Functions from C into Banach Algebras 29
Exercise 33
References 33
Chapter 3 Regular Points and Spectrum 34
Compactness of the Spectrum 38
Introduction to the Gel fand Theory of Commutative Banach
Algebras 48
The Quotient Algebra 50
Exercises 53
References 54
Chapter 4 More on the Gel fand Theory and an Intro¬
duction to Point Set Topology 55
Topology 60
A Topological Space 61
vii
viii Contents
Examples of Topological Spaces 61
Further Topological Notions 62
The Neighborhood Approach 66
Exercises 71
References 72
Chapter 5 Further Topological Notions 73
Bases, Fundamental Systems of Neighborhoods, and Subbases 73
The Relative Topology and Product Spaces 78
Separation Axioms and Compactness 79
The Tychonoff Theorem and Locally Compact Spaces 84
A Neighborhood Topology for the Set of Maximal Ideals over a
Banach Algebra 87
Exercises 89
References 90
Chapter 6 Compactness of the Space of Maximal Ideals
over a Banach Algebra; an Introduction to
Topological Groups and Star Algebras 91
Star Algebras 97
Topological Groups 98
Exercises 106
References 106
Chapter 7 The Quotient Group of a Topological Group
and Some Further Topological Notions 107
Locally Compact Topological Groups 107
Subgroups and Quotient Groups 109
Directed Sets and Generalized Sequences 116
Further Topological Notions 117
Exercises 123
References 124
Chapter 8 Right Haar Measures and the Haar Covering
Function 125
Notation and Some Measure Theoretic Results 125
The Haar Covering Function 129
Summary of Theorems in Chapter 8 ,... 147
Exercises 149
References 149
Contents ix
Chapter 9 The Existence of a Right Invariant Haar
Integral over any Locally Compact Topolog
ical Group 150
The Daniell Extension Approach 158
A Measure Theoretic Approach 160
Appendix to Chapter 9 163
Exercises 164
References 165
Chapter 10 The Daniell Extension from a Topological
Point of View, Some General Results from
Measure Theory, and Group Algebras 166
Extending the Integral 166
Uniqueness of the Integral 169
Examples of Haar Measures 172
Product Measures 176
Exercises 186
References 187
Chapter 11 Characters and the Dual Group of a Locally
Compact, Abelian, Topological Group 188
Characters and the Dual Group 192
Examples of Characters 200
Exercises 206
References 206
Chapter 12 Generalization of the Fourier Transform to
LJG) and L2(G) 207
The Fourier Transform on Li(G) 207
Complex Measures 211
The Fourier Stieltjes Transform 219
Positive Definite Functions 220
The Fourier Transform on Li(G) 235
Exercises 243
Appendix to Chapter 12 244
References 250
BIBLIOGRAPHY 251
INDEX 253
|
| adam_txt |
Contents
PREFACE V
SYMBOLS USED IN TEXT X
Chapter 1 The Fourier Transform on the Real Line for
Functions in L] 1
Introduction 1
Notation 1
The Fourier Transform 2
Recovery 4
Relation between the Norms of the Fourier Transform and the
Function 10
Appendix to Chapter 1 15
Exercises 17
References 18
Chapter 2 The Fourier Transform on the Real Line for
Functions in L2 19
Inversion in h% 21
Normed and Banach Algebras 25
Analytic Properties of Functions from C into Banach Algebras 29
Exercise 33
References 33
Chapter 3 Regular Points and Spectrum 34
Compactness of the Spectrum 38
Introduction to the Gel'fand Theory of Commutative Banach
Algebras 48
The Quotient Algebra 50
Exercises 53
References 54
Chapter 4 More on the Gel'fand Theory and an Intro¬
duction to Point Set Topology 55
Topology 60
A Topological Space 61
vii
viii Contents
Examples of Topological Spaces 61
Further Topological Notions 62
The Neighborhood Approach 66
Exercises 71
References 72
Chapter 5 Further Topological Notions 73
Bases, Fundamental Systems of Neighborhoods, and Subbases 73
The Relative Topology and Product Spaces 78
Separation Axioms and Compactness 79
The Tychonoff Theorem and Locally Compact Spaces 84
A Neighborhood Topology for the Set of Maximal Ideals over a
Banach Algebra 87
Exercises 89
References 90
Chapter 6 Compactness of the Space of Maximal Ideals
over a Banach Algebra; an Introduction to
Topological Groups and Star Algebras 91
Star Algebras 97
Topological Groups 98
Exercises 106
References 106
Chapter 7 The Quotient Group of a Topological Group
and Some Further Topological Notions 107
Locally Compact Topological Groups 107
Subgroups and Quotient Groups 109
Directed Sets and Generalized Sequences 116
Further Topological Notions 117
Exercises 123
References 124
Chapter 8 Right Haar Measures and the Haar Covering
Function 125
Notation and Some Measure Theoretic Results 125
The Haar Covering Function 129
Summary of Theorems in Chapter 8 ,. 147
Exercises 149
References 149
Contents ix
Chapter 9 The Existence of a Right Invariant Haar
Integral over any Locally Compact Topolog
ical Group 150
The Daniell Extension Approach 158
A Measure Theoretic Approach 160
Appendix to Chapter 9 163
Exercises 164
References 165
Chapter 10 The Daniell Extension from a Topological
Point of View, Some General Results from
Measure Theory, and Group Algebras 166
Extending the Integral 166
Uniqueness of the Integral 169
Examples of Haar Measures 172
Product Measures 176
Exercises 186
References 187
Chapter 11 Characters and the Dual Group of a Locally
Compact, Abelian, Topological Group 188
Characters and the Dual Group 192
Examples of Characters 200
Exercises 206
References 206
Chapter 12 Generalization of the Fourier Transform to
LJG) and L2(G) 207
The Fourier Transform on Li(G) 207
Complex Measures 211
The Fourier Stieltjes Transform 219
Positive Definite Functions 220
The Fourier Transform on Li(G) 235
Exercises 243
Appendix to Chapter 12 244
References 250
BIBLIOGRAPHY 251
INDEX 253 |
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| spelling | Bachman, George Verfasser aut Elements of abstract harmonic analysis by George Bachman 2. print. New York [u.a.] Acad. Press 1965 XI, 250 S. txt rdacontent n rdamedia nc rdacarrier Academic paperbacks : Mathematics Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Harmonische Analyse (DE-588)4023453-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015137506&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4023453-8 (DE-588)4151278-9 |
| title | Elements of abstract harmonic analysis |
| title_auth | Elements of abstract harmonic analysis |
| title_exact_search | Elements of abstract harmonic analysis |
| title_exact_search_txtP | Elements of abstract harmonic analysis |
| title_full | Elements of abstract harmonic analysis by George Bachman |
| title_fullStr | Elements of abstract harmonic analysis by George Bachman |
| title_full_unstemmed | Elements of abstract harmonic analysis by George Bachman |
| title_short | Elements of abstract harmonic analysis |
| title_sort | elements of abstract harmonic analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonische Analyse Einführung |
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