Integrals and operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | Undetermined |
| Published: |
Berlin [u.a.]
Springer
1978
|
| Edition: | 2., rev. and enl. ed. |
| Series: | Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen
228 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 321 S. |
| ISBN: | 3540083235 0387083235 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804136091973844992 |
|---|---|
| adam_text | CONTENTS
CHAPTER I. INTRODUCTION 1
1.1 General preliminaries 1
1.2 The idea of measure 3
1.3 Integration as a technique in analysis 7
1.4 Limitations on the concept of measure space 12
1.5 Generalized spectral theory and measure spaces 13
Exercises 15
CHAPTER II. BASIC INTEGRALS 18
2.1 Basic measure spaces 18
2.2 The basic Lebesgue Stieltjes spaces 20
Exercises 26
2.3 Integrals of step functions 28
Exercises 31
2.4 Products of basic spaces 32
xi
xii Contents
2.5* Coin tossing space 34
Exercises 36
2.6 Infinity in integration theory 36
Exercises 41
CHAPTER III. MEASURABLE FUNCTIONS AND THEIR
INTEGRALS 43
3.1 The extension problem 43
3.2 Measurability relative to a basic ring 44
Exercises 54
3.3 The integral 54
Exercises 65
3.4 Development of the integral 66
Exercises 73
3.5 Extensions and completions of measure spaces 76
Exercises 80
3.6 Multiple integration 83
Exercises 87
3.7 Large spaces 89
Exercises 91
CHAPTER IV. CONVERGENCE AND DIFFERENTIATION 93
4.1 Linear spaces of measurable functions 93
Exercises 105
4.2 Set functions 107
Exercises 112
4.3 Differentiation of set functions 114
Exercises 121
CHAPTER V. LOCALLY COMPACT AND EUCLIDEAN SPACES 123
5.1 Functions on locally compact spaces 123
Exercises 128
5.2 Measures in locally compact spaces 128
Exercises 133
5.3 Transformation of Lebesgue measure 136
Exercises 143
5.4 Set functions and differentiation in euclidean space 143
Exercises 149
Contents xiii
CHAPTER VI. FUNCTION SPACES 152
6.1 Linear duality 152
Exercises 165
6.2 Vector valued functions 168
Exercises 173
CHAPTER VII. INVARIANT INTEGRALS 175
7.1 Introduction 175
7.2 Transformation groups 178
Exercises 179
7.3 Uniform spaces 181
Exercises 187
7.4 The Haar integral 187
7.5 Developments from uniqueness 193
Exercises 196
7.6 Function spaces under group action 199
Exercises 203
CHAPTER VIII. ALGEBRAIC INTEGRATION THEORY 206
8.1 Introduction 206
8.2 Banach algebras and the characterization of function algebras 208
Exercises 219
8.3 Introductory features of Hilbert spaces 221
Exercises 231
8.4 Integration algebras 233
Exercises 237
CHAPTER IX. SPECTRAL ANALYSIS IN HILBERT SPACE 239
9.1 Introduction 239
9.2 The structure of maximal Abelian self adjoint algebras 241
Exercises 253
CHAPTER X. GROUP REPRESENTATIONS AND UNBOUNDED
OPERATORS 258
10.1 Representations of locally compact groups 258
10.2 Representations of Abelian groups 265
Exercises 273
10.3 Unbounded diagonalizable operators 276
Exercises 288
10.4 Abelian harmonic analysis 290
Exercises 299
xiv Contents
CHAPTER XI. SEMIGROUPS AND PERTURBATION THEORY 303
11.1 Introduction 303
11.2 The Hille Yosida theorem 303
11.3 Convergence of semigroups 307
11.4 Strong convergence of self adjoint operators 312
11.5 Rellich Kato perturbations 316
Exercises 317
11.6 Perturbations in a calibrated space 318
Exercises 322
CHAPTER XII. OPERATOR RINGS AND SPECTRAL
MULTIPLICITY 324
12.1 Introduction 324
12.2 The double commutor theorem 325
Exercises 329
12.3 The structure of abelian rings 330
Exercises 337
CHAPTER XIII. C* ALGEBRAS AND APPLICATIONS 340
13.1 Introduction 340
13.2 Representations and states 341
Exercises 349
CHAPTER XIV. THE TRACE AS A NON COMMUTATIVE
INTEGRAL 351
14.1 Introduction 351
14.2 Elementary operators and the trace 352
Exercises 356
14.3 Hilbert algebras 357
Exercises 363
Selected references 365
Index 369
|
| adam_txt |
CONTENTS
CHAPTER I. INTRODUCTION 1
1.1 General preliminaries 1
1.2 The idea of measure 3
1.3 Integration as a technique in analysis 7
1.4 Limitations on the concept of measure space 12
1.5 Generalized spectral theory and measure spaces 13
Exercises 15
CHAPTER II. BASIC INTEGRALS 18
2.1 Basic measure spaces 18
2.2 The basic Lebesgue Stieltjes spaces 20
Exercises 26
2.3 Integrals of step functions 28
Exercises 31
2.4 Products of basic spaces 32
xi
xii Contents
2.5* Coin tossing space 34
Exercises 36
2.6 Infinity in integration theory 36
Exercises 41
CHAPTER III. MEASURABLE FUNCTIONS AND THEIR
INTEGRALS 43
3.1 The extension problem 43
3.2 Measurability relative to a basic ring 44
Exercises 54
3.3 The integral 54
Exercises 65
3.4 Development of the integral 66
Exercises 73
3.5 Extensions and completions of measure spaces 76
Exercises 80
3.6 Multiple integration 83
Exercises 87
3.7 Large spaces 89
Exercises 91
CHAPTER IV. CONVERGENCE AND DIFFERENTIATION 93
4.1 Linear spaces of measurable functions 93
Exercises 105
4.2 Set functions 107
Exercises 112
4.3 Differentiation of set functions 114
Exercises 121
CHAPTER V. LOCALLY COMPACT AND EUCLIDEAN SPACES 123
5.1 Functions on locally compact spaces 123
Exercises 128
5.2 Measures in locally compact spaces 128
Exercises 133
5.3 Transformation of Lebesgue measure 136
Exercises 143
5.4 Set functions and differentiation in euclidean space 143
Exercises 149
Contents xiii
CHAPTER VI. FUNCTION SPACES 152
6.1 Linear duality 152
Exercises 165
6.2 Vector valued functions 168
Exercises 173
CHAPTER VII. INVARIANT INTEGRALS 175
7.1 Introduction 175
7.2 Transformation groups 178
Exercises 179
7.3 Uniform spaces 181
Exercises 187
7.4 The Haar integral 187
7.5 Developments from uniqueness 193
Exercises 196
7.6 Function spaces under group action 199
Exercises 203
CHAPTER VIII. ALGEBRAIC INTEGRATION THEORY 206
8.1 Introduction 206
8.2 Banach algebras and the characterization of function algebras 208
Exercises 219
8.3 Introductory features of Hilbert spaces 221
Exercises 231
8.4 Integration algebras 233
Exercises 237
CHAPTER IX. SPECTRAL ANALYSIS IN HILBERT SPACE 239
9.1 Introduction 239
9.2 The structure of maximal Abelian self adjoint algebras 241
Exercises 253
CHAPTER X. GROUP REPRESENTATIONS AND UNBOUNDED
OPERATORS 258
10.1 Representations of locally compact groups 258
10.2 Representations of Abelian groups 265
Exercises 273
10.3 Unbounded diagonalizable operators 276
Exercises 288
10.4 Abelian harmonic analysis 290
Exercises 299
xiv Contents
CHAPTER XI. SEMIGROUPS AND PERTURBATION THEORY 303
11.1 Introduction 303
11.2 The Hille Yosida theorem 303
11.3 Convergence of semigroups 307
11.4 Strong convergence of self adjoint operators 312
11.5 Rellich Kato perturbations 316
Exercises 317
11.6 Perturbations in a calibrated space 318
Exercises 322
CHAPTER XII. OPERATOR RINGS AND SPECTRAL
MULTIPLICITY 324
12.1 Introduction 324
12.2 The double commutor theorem 325
Exercises 329
12.3 The structure of abelian rings 330
Exercises 337
CHAPTER XIII. C* ALGEBRAS AND APPLICATIONS 340
13.1 Introduction 340
13.2 Representations and states 341
Exercises 349
CHAPTER XIV. THE TRACE AS A NON COMMUTATIVE
INTEGRAL 351
14.1 Introduction 351
14.2 Elementary operators and the trace 352
Exercises 356
14.3 Hilbert algebras 357
Exercises 363
Selected references 365
Index 369 |
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| author | Segal, Irving Ezra 1918-1998 Kunze, Ray Alden 1928-2014 |
| author_GND | (DE-588)119350211 (DE-588)109029046 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2., rev. and enl. ed. |
| format | Book |
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| id | DE-604.BV022118395 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:07Z |
| indexdate | 2024-07-09T20:50:54Z |
| institution | BVB |
| isbn | 3540083235 0387083235 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015333261 |
| oclc_num | 634928796 |
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| owner | DE-706 |
| owner_facet | DE-706 |
| physical | 321 S. |
| publishDate | 1978 |
| publishDateSearch | 1978 |
| publishDateSort | 1978 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |
| series2 | Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen |
| spelling | Segal, Irving Ezra 1918-1998 Verfasser (DE-588)119350211 aut Integrals and operators Irving E. Segal ; Ray A. Kunze 2., rev. and enl. ed. Berlin [u.a.] Springer 1978 321 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 228 Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Integral (DE-588)4131477-3 gnd rswk-swf Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Integration Mathematik (DE-588)4072852-3 s Operator (DE-588)4130529-2 s Topologische Gruppe (DE-588)4135793-0 s Operatortheorie (DE-588)4075665-8 s 1\p DE-604 Integral (DE-588)4131477-3 s 2\p DE-604 Kunze, Ray Alden 1928-2014 Verfasser (DE-588)109029046 aut Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen 228 (DE-604)BV000000395 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015333261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Segal, Irving Ezra 1918-1998 Kunze, Ray Alden 1928-2014 Integrals and operators Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen Operatortheorie (DE-588)4075665-8 gnd Operator (DE-588)4130529-2 gnd Topologische Gruppe (DE-588)4135793-0 gnd Integral (DE-588)4131477-3 gnd Integration Mathematik (DE-588)4072852-3 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4130529-2 (DE-588)4135793-0 (DE-588)4131477-3 (DE-588)4072852-3 (DE-588)4018916-8 |
| title | Integrals and operators |
| title_auth | Integrals and operators |
| title_exact_search | Integrals and operators |
| title_exact_search_txtP | Integrals and operators |
| title_full | Integrals and operators Irving E. Segal ; Ray A. Kunze |
| title_fullStr | Integrals and operators Irving E. Segal ; Ray A. Kunze |
| title_full_unstemmed | Integrals and operators Irving E. Segal ; Ray A. Kunze |
| title_short | Integrals and operators |
| title_sort | integrals and operators |
| topic | Operatortheorie (DE-588)4075665-8 gnd Operator (DE-588)4130529-2 gnd Topologische Gruppe (DE-588)4135793-0 gnd Integral (DE-588)4131477-3 gnd Integration Mathematik (DE-588)4072852-3 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Operatortheorie Operator Topologische Gruppe Integral Integration Mathematik Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015333261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT segalirvingezra integralsandoperators AT kunzerayalden integralsandoperators |