Elements of applicable functional analysis
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Dekker
1980
|
| Schriftenreihe: | Pure and applied mathematics
55 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Groetsch, Charles W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elements of applicable functional analysis |c Charles W. Groetsch |
| 264 | 1 | |a New York, NY [u.a.] |b Dekker |c 1980 | |
| 300 | |a X, 300 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 55 | |
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 4 | |a Commande | |
| 650 | 4 | |a Equation intégrale | |
| 650 | 4 | |a Exercice analyse | |
| 650 | 4 | |a Fonction spline | |
| 650 | 4 | |a Méthode variationnelle | |
| 650 | 4 | |a Optimisation | |
| 650 | 4 | |a Opérateur non linéaire | |
| 650 | 4 | |a Programmation convexe | |
| 650 | 4 | |a Théorie spectrale | |
| 650 | 4 | |a Functional analysis | |
| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Pure and applied mathematics |v 55 |w (DE-604)BV000001885 |9 55 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-001303694 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 460f 2001 A 16338 |
|---|---|
| DE-BY-TUM_katkey | 187159 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010349601 |
| _version_ | 1820872468431110144 |
| adam_text | CONTENTS
Preface v
I. METRIC SPACES 1
1. Basic Concepts 1
2. Convergence, Completeness and Compactness 5
3. Existence Theorems in Differential Equations
and the Calculus of Variations 10
Exercises 21
II. BANACH SPACES 26
1. Linear Spaces and Norms 26
2. Convex Sets, Subspaces and Quotient Spaces 30
3. Linear Functionals and the Dual Space 33
4. Some Classical Banach Spaces 42
5. The Uniform Boundedness Theorem and Applications 49
6. The Open Mapping Theorem 57
7. Sard s Theorem and the Peano Kernel 59
8. Optimization and Convex Programming 65
9. Extreme Points and Control 76
Exercises 84
III. HILBERT SPACES 92
1. Basic Results 92
2. Orthogonal Expansions 100
3. Linear Operators 109
4. Bilinear Forms and the Lax Milgram Lemma 121
Exercises 126
ix
x CONTENTS
IV. COMPACT OPERATORS 136
1. General Considerations 136
2. Compact Operators in Hilbert Space 139
3. Integral Equations and Boundary
Value Problems 149
4. Collectively Compact Operators and
Numerical Solutions of Integral Equations 163
Exercises 168
V. THE SPECTRAL THEOREM 175
1. Positive Operators 175
2. The Spectral Decomposition 179
3. The Operator Calculus 189
Exercises 193
VI. VARIATIONAL METHODS 195
1. Quadratic Functionals and the Friedrichs
Construction 195
2. The Ritz Galerkin Method 202
3. The Eigenvalue Problem 205
4. Sard s Generalized Splines 215
5. Least Squares, Generalized Inverses
and Regularization 221
Exercises 227
VII. NONLINEAR OPERATORS 271
1. Contractive Mappings 231
2. Differentiation of Operators 240
3. Newton s Method 252
Exercises 263
APPENDIXES 271
A. Notions from Set Theory 271
B. The Weierstrass Theorem 275
C. Topology and Tikhonov s Theorem 281
D. The Riemann Stieljes Integral 285
BIBLIOGRAPHY 291
INDEX 297
|
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| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)6222712 (DE-599)BVBBV001998591 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001998591 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-23T10:27:36Z |
| institution | BVB |
| isbn | 0824769864 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001303694 |
| oclc_num | 6222712 |
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| physical | X, 300 S. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spellingShingle | Groetsch, Charles W. Elements of applicable functional analysis Pure and applied mathematics Analyse fonctionnelle Analyse fonctionnelle ram Commande Equation intégrale Exercice analyse Fonction spline Méthode variationnelle Optimisation Opérateur non linéaire Programmation convexe Théorie spectrale Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Elements of applicable functional analysis |
| title_auth | Elements of applicable functional analysis |
| title_exact_search | Elements of applicable functional analysis |
| title_full | Elements of applicable functional analysis Charles W. Groetsch |
| title_fullStr | Elements of applicable functional analysis Charles W. Groetsch |
| title_full_unstemmed | Elements of applicable functional analysis Charles W. Groetsch |
| title_short | Elements of applicable functional analysis |
| title_sort | elements of applicable functional analysis |
| topic | Analyse fonctionnelle Analyse fonctionnelle ram Commande Equation intégrale Exercice analyse Fonction spline Méthode variationnelle Optimisation Opérateur non linéaire Programmation convexe Théorie spectrale Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Commande Equation intégrale Exercice analyse Fonction spline Méthode variationnelle Optimisation Opérateur non linéaire Programmation convexe Théorie spectrale Functional analysis Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303694&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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