Functional analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2018]
|
| Schriftenreihe: | Graduate studies in mathematics
191 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 466 Seiten Diagramme |
| ISBN: | 9781470441906 |
Internformat
MARC
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| 245 | 1 | 0 | |a Functional analysis |c Theo Bühler, Dietmar A. Salamon |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2018] | |
| 264 | 4 | |c © 2018 | |
| 300 | |a xiv, 466 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 191 | |
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Datensatz im Suchindex
| _version_ | 1804178506906599424 |
|---|---|
| adam_text | Contents
Preface ix
Introduction xi
Chapter 1. Foundations 1
§1.1. Metric Spaces and Compact Sets 2
§1.2. Finite-Dimensional Banach Spaces 17
§1.3. The Dual Space 25
§1.4. Hilbert Spaces 31
§1.5. Banach Algebras 35
§1.6. The Baire Category Theorem 40
§1.7. Problems 45
Chapter 2. Principles of Functional Analysis 49
§2.1. Uniform Boundedness 50
§2.2. Open Mappings and Closed Graphs 54
§2.3. Hahn-Banach and Convexity 65
§2.4. Reflexive Banach Spaces 80
§2.5. Problems 101
Chapter 3. The Weak and Weak* Topologies 109
§3.1. Topological Vector Spaces 110
§3.2. The Banach-Alaoglu Theorem 124
§3.3. The Banach-Dieudonne Theorem 130
§3.4. The Eberlein-Smulyan Theorem 134
v
VI
Contents
§3.5. The Kreïn-Milman Theorem
§3.6. Ergodic Theory
§3.7. Problems
Chapter 4. Fredholm Theory
§4.1. The Dual Operator
§4.2. Compact Operators
§4.3. Fredholm Operators
§4.4. Composition and Stability
§4.5. Problems
Chapter 5. Spectral Theory
§5.1. Complex Banach Spaces
§5.2. Spectrum
§5.3. Operators on Hilbert Spaces
§5.4. Functional Calculus for Self-Adjoint Operators
§5.5. Gelfand Spectrum and Normal Operators
§5.6. Spectral Measures
§5.7. Cyclic Vectors
§5.8. Problems
Chapter 6. Unbounded Operators
§6.1. Unbounded Operators on Banach Spaces
§6.2. The Dual of an Unbounded Operator
§6.3. Unbounded Operators on Hilbert Spaces
§6.4. Functional Calculus and Spectral Measures
§6.5. Problems
140
144
153
163
164
173
179
184
189
197
198
208
222
234
246
261
281
288
295
295
306
313
326
342
Chapter 7. Semigroups of Operators 349
§7.1. Strongly Continuous Semigroups 350
§7.2. The Hille-Yosida-Phillips Theorem 363
§7.3. The Dual Semigroup 377
§7.4. Analytic Semigroups 388
§7.5. Banach Space Valued Measurable Functions 404
§7.6. Inhomogeneous Equations 425
§7.7. Problems 439
Contents vii
Appendix A. Zorn and Tychonoff 445
§A.l. The Lemma of Zorn 445
§A.2. Tychonoff’s Theorem 449
Bibliography 453
Notation 459 •
Index
461
|
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| id | DE-604.BV044930841 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:05:04Z |
| institution | BVB |
| isbn | 9781470441906 |
| language | English |
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| oclc_num | 1043870574 |
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| physical | xiv, 466 Seiten Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Bühler, Theo 1978- Verfasser (DE-588)1033205508 aut Functional analysis Theo Bühler, Dietmar A. Salamon Providence, Rhode Island American Mathematical Society [2018] © 2018 xiv, 466 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 191 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Salamon, Dietmar 1953- Verfasser (DE-588)1015895271 aut Graduate studies in mathematics 191 (DE-604)BV009739289 191 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=030323908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bühler, Theo 1978- Salamon, Dietmar 1953- Functional analysis Graduate studies in mathematics Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4123623-3 |
| title | Functional analysis |
| title_auth | Functional analysis |
| title_exact_search | Functional analysis |
| title_full | Functional analysis Theo Bühler, Dietmar A. Salamon |
| title_fullStr | Functional analysis Theo Bühler, Dietmar A. Salamon |
| title_full_unstemmed | Functional analysis Theo Bühler, Dietmar A. Salamon |
| title_short | Functional analysis |
| title_sort | functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030323908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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