Lecture notes on functional analysis: with applications to linear partial differential equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2013
|
| Schriftenreihe: | Graduate studies in mathematics
143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 245 - 246 |
| Beschreibung: | XII, 250 S. graph. Darst. |
| ISBN: | 9780821887714 |
Internformat
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| 245 | 1 | 0 | |a Lecture notes on functional analysis |b with applications to linear partial differential equations |c Alberto Bressan |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2013 | |
| 300 | |a XII, 250 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 143 | |
| 500 | |a Literaturverz. S. 245 - 246 | ||
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| 650 | 4 | |a Differential equations, Linear | |
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Datensatz im Suchindex
| _version_ | 1804149696549093376 |
|---|---|
| adam_text | Titel: Lecture notes on functional analysis
Autor: Bressan, Alberto
Jahr: 2013
Contents
Preface xi
Chapter 1. Introduction 1
§1.1. Linear equations 1
§1.2. Evolution equations 4
§1.3. Function spaces 7
§1.4. Compactness 7
Chapter 2. Banach Spaces 11
§2.1. Basic definitions 11
§2.2. Linear operators 16
§2.3. Finite-dimensional spaces 20
§2.4. Seminorms and Fréchet spaces 23
§2.5. Extension theorems 26
§2.6. Separation of convex sets 30
§2.7. Dual spaces and weak convergence 32
§2.8. Problems 35
Chapter 3. Spaces of Continuous Functions 45
§3.1. Bounded continuous functions 45
§3.2. The Stone-Weierstrass approximation theorem 47
§3.3. Ascoli s compactness theorem 53
§3.4. Spaces of Holder continuous functions 56
§3.5. Problems 57
vi i
viii
Contents
Chapter 4. Bounded Linear Operators 1
§4.1. The uniform boundedness principle 61
§4.2. The open mapping theorem 63
§4.3. The closed graph theorem 64
§4.4. Adjoint operators 66
§4.5. Compact operators 68
§4.6. Problems 71
Chapter 5. Hilbert Spaces 77
§5.1. Spaces with an inner product 78
§5.2. Orthogonal projections 79
§5.3. Linear functionals on a Hilbert space 82
§5.4. Gram-Schmidt orthogonalization 84
§5.5. Orthonormal sets 85
§5.6. Positive definite operators 89
§5.7. Weak convergence 92
§5.8. Problems 95
Chapter 6. Compact Operators on a Hilbert Space 101
§6.1. Fredholm theory 101
§6.2. Spectrum of a compact operator 106
§6.3. Selfadjoint operators 107
§6.4. Problems 111
Chapter 7. Semigroups of Linear Operators 115
§7.1. Ordinary differential equations in a Banach space 115
§7.2. Semigroups of linear operators 120
§7.3. Resolvents 124
§7.4. Generation of a semigroup 128
§7.5. Problems 134
Chapter 8. Sobolev Spaces 139
§8.1. Distributions and weak derivatives 139
§8.2. Mollifications 14g
§8.3. Sobolev spaces 151
§8.4. Approximations of Sobolev functions 157
§8.5. Extension operators 151
§8.6. Embedding theorems 153
Contents
ix
§8.7. Compact embeddings 175
§8.8. Differentiability properties 179
§8.9. Problems 180
Chapter 9. Linear Partial Differential Equations 185
§9.1. Elliptic equations 185
§9.2. Parabolic equations 200
§9.3. Hyperbolic equations 207
§9.4. Problems 212
Appendix. Background Material 217
§A.l. Partially ordered sets 217
§A.2. Metric and topological spaces 217
§A.3. Review of Lebesgue measure theory 222
§A.4. Integrals of functions taking values in a Banach space 226
§A.5. Mollifications 228
§A.6. Inequalities 233
§A.7. Problems 237
Summary of Notation 241
Bibliography 245
Index ^7
|
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| dewey-sort | 3515 17 |
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| discipline | Mathematik |
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| isbn | 9780821887714 |
| language | English |
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| spelling | Bressan, Alberto 1956- Verfasser (DE-588)172009952 aut Lecture notes on functional analysis with applications to linear partial differential equations Alberto Bressan Providence, RI American Math. Soc. 2013 XII, 250 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 143 Literaturverz. S. 245 - 246 Functional analysis Differential equations, Linear Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) msc Partial differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) msc Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Graduate studies in mathematics 143 (DE-604)BV009739289 143 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bressan, Alberto 1956- Lecture notes on functional analysis with applications to linear partial differential equations Graduate studies in mathematics Functional analysis Differential equations, Linear Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) msc Partial differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) msc Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Lecture notes on functional analysis with applications to linear partial differential equations |
| title_auth | Lecture notes on functional analysis with applications to linear partial differential equations |
| title_exact_search | Lecture notes on functional analysis with applications to linear partial differential equations |
| title_full | Lecture notes on functional analysis with applications to linear partial differential equations Alberto Bressan |
| title_fullStr | Lecture notes on functional analysis with applications to linear partial differential equations Alberto Bressan |
| title_full_unstemmed | Lecture notes on functional analysis with applications to linear partial differential equations Alberto Bressan |
| title_short | Lecture notes on functional analysis |
| title_sort | lecture notes on functional analysis with applications to linear partial differential equations |
| title_sub | with applications to linear partial differential equations |
| topic | Functional analysis Differential equations, Linear Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) msc Partial differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) msc Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Differential equations, Linear Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) Partial differential equations -- Instructional exposition (textbooks, tutorial papers, etc.) Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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