A friendly approach to functional analysis
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| Format: | Buch |
| Sprache: | English |
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New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo
World Scientific
[2017]
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| Schriftenreihe: | Essential textbooks in mathematics
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| 003 | DE-604 | ||
| 005 | 20211119 | ||
| 007 | t | ||
| 008 | 171103s2017 a||| |||| 00||| eng d | ||
| 020 | |a 9781786343338 |c hbk |9 978-1-78634-333-8 | ||
| 020 | |a 9781786343345 |c pbk |9 978-1-78634-334-5 | ||
| 035 | |a (OCoLC)993613772 | ||
| 035 | |a (DE-599)OBVAC13671020 | ||
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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 | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Essential textbooks in mathematics | |
| 500 | |a Literaturverzeichnis: Seite 373-374 | ||
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-029974484 | ||
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102/MAT 460f 2017 A 5138 |
|---|---|
| DE-BY-TUM_katkey | 2292297 |
| DE-BY-TUM_media_number | 040008682826 |
| _version_ | 1816714363433648128 |
| 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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| classification_rvk | SK 600 |
| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)993613772 (DE-599)OBVAC13671020 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044575963 |
| illustrated | Illustrated |
| indexdate | 2024-11-25T17:51:13Z |
| institution | BVB |
| isbn | 9781786343338 9781786343345 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029974484 |
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| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-739 DE-384 DE-634 DE-83 |
| physical | xiv, 379 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | World Scientific |
| record_format | marc |
| series2 | Essential textbooks in mathematics |
| 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 |
| url | http://media.obvsg.at/AC13671020-1001 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 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 |
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