A friendly approach to functional analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2017]
|
| Schriftenreihe: | Essential textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 373-374 |
| Beschreibung: | xiv, 379 Seiten Illustrationen, Diagramme |
| ISBN: | 9781786343338 9781786343345 |
Internformat
MARC
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| 100 | 1 | |a Sasane, Amol |d 1976- |0 (DE-588)1049615182 |4 aut | |
| 245 | 1 | 0 | |a A friendly approach to functional analysis |c Amol Sasane ; London School of Economics, UK |
| 264 | 1 | |a New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo |b World Scientific |c [2017] | |
| 300 | |a xiv, 379 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Essential textbooks in mathematics | |
| 500 | |a Literaturverzeichnis: Seite 373-374 | ||
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Datensatz im Suchindex
| _version_ | 1804177959759642624 |
|---|---|
| adam_text | Contents
Preface vii
1. Normed and Banach spaces 1
1.1 Vector spaces .......................................... 3
1.2 Normed spaces........................................... 7
1.3 Topology of normed spaces.............................. 17
1.4 Sequences in a normed space; Banach spaces............. 24
1.5 Compact sets........................................... 44
2. Continuous and linear maps 53
2.1 Linear transformations................................. 54
2.2 Continuous maps....................................... 58
2.3 The normed space CL(X^Y)............................... 67
2.4 Composition of continuous linear transformations....... 82
2.5 (*) Open Mapping Theorem............................... 92
2.6 Spectral Theory........................................ 97
2.7 (*) Dual space and the Hahn-Banach Theorem............ 104
3. Differentiation 117
3.1 Definition of the derivative ......................... 118
3.2 Fundamental theorems of optimisation.................. 125
3.3 Euler-Lagrange equation.............................. 134
3.4 An excursion in Classical Mechanics................... 145
4. Geometry of inner product spaces 155
4.1 Inner product spaces.................................. 156
xiii
xiv A Friendly Approach to Functional Analysis
4.2 Orthogonality............................................. 165
4.3 Best approximation........................................ 174
4.4 Generalised Fourier series................................ 183
4.5 Riesz Representation Theorem.............................. 189
4.6 Adjoints of bounded operators ............................ 190
4.7 An excursion in Quantum Mechanics..........................200
5. Compact operators 209
5.1 Compact operators......................................... 210
5.2 The set K(Xy Y) of all compact operators.................. 211
5.3 Approximation of compact operators........................ 217
5.4 (*) Spectral Theorem for Compact Operators................ 222
6. A glimpse of distribution theory 227
6.1 Test functions, distributions, and examples............... 230
6.2 Derivatives in the distributional sense .................. 237
6.3 Weak solutions............................................ 243
6.4 Multiplication by C°° functions........................... 248
6.5 Fourier transform of (tempered) distributions............. 253
Solutions 259
The Lebesgue integral 359
Bibliography 373
Index 375
Contents
Preface vii
1. Normed and Banach spaces 1
1.1 Vector spaces .......................................... 3
1.2 Normed spaces........................................... 7
1.3 Topology of normed spaces.............................. 17
1.4 Sequences in a normed space; Banach spaces............. 24
1.5 Compact sets........................................... 44
2. Continuous and linear maps 53
2.1 Linear transformations................................. 54
2.2 Continuous maps....................................... 58
2.3 The normed space CL(X^Y)............................... 67
2.4 Composition of continuous linear transformations....... 82
2.5 (*) Open Mapping Theorem............................... 92
2.6 Spectral Theory........................................ 97
2.7 (*) Dual space and the Hahn-Banach Theorem............ 104
3. Differentiation 117
3.1 Definition of the derivative ......................... 118
3.2 Fundamental theorems of optimisation.................. 125
3.3 Euler-Lagrange equation.............................. 134
3.4 An excursion in Classical Mechanics................... 145
4. Geometry of inner product spaces 155
4.1 Inner product spaces.................................. 156
xiii
xiv A Friendly Approach to Functional Analysis
4.2 Orthogonality............................................. 165
4.3 Best approximation........................................ 174
4.4 Generalised Fourier series................................ 183
4.5 Riesz Representation Theorem.............................. 189
4.6 Adjoints of bounded operators ............................ 190
4.7 An excursion in Quantum Mechanics..........................200
5. Compact operators 209
5.1 Compact operators......................................... 210
5.2 The set K(Xy Y) of all compact operators.................. 211
5.3 Approximation of compact operators........................ 217
5.4 (*) Spectral Theorem for Compact Operators................ 222
6. A glimpse of distribution theory 227
6.1 Test functions, distributions, and examples............... 230
6.2 Derivatives in the distributional sense .................. 237
6.3 Weak solutions............................................ 243
6.4 Multiplication by C°° functions........................... 248
6.5 Fourier transform of (tempered) distributions............. 253
Solutions 259
The Lebesgue integral 359
Bibliography 373
Index 375
|
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| id | DE-604.BV044575963 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:56:22Z |
| institution | BVB |
| isbn | 9781786343338 9781786343345 |
| language | English |
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| physical | xiv, 379 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
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| publisher | World Scientific |
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| series2 | Essential textbooks in mathematics |
| spelling | Sasane, Amol 1976- (DE-588)1049615182 aut A friendly approach to functional analysis Amol Sasane ; London School of Economics, UK New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific [2017] xiv, 379 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Essential textbooks in mathematics Literaturverzeichnis: Seite 373-374 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 V:AT-OBV;B:AT-UBTUW application/pdf http://media.obvsg.at/AC13671020-1001 Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029974484&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029974484&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sasane, Amol 1976- A friendly approach to functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | A friendly approach to functional analysis |
| title_auth | A friendly approach to functional analysis |
| title_exact_search | A friendly approach to functional analysis |
| title_full | A friendly approach to functional analysis Amol Sasane ; London School of Economics, UK |
| title_fullStr | A friendly approach to functional analysis Amol Sasane ; London School of Economics, UK |
| title_full_unstemmed | A friendly approach to functional analysis Amol Sasane ; London School of Economics, UK |
| title_short | A friendly approach to functional analysis |
| title_sort | a friendly approach to functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis |
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