Applied functional analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Edition: | 2. ed. |
| Series: | Pure and applied mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Franz. übers. |
| Physical Description: | XVI, 495 S. |
| ISBN: | 0471179760 |
Staff View
MARC
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| 100 | 1 | |a Aubin, Jean-Pierre |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied functional analysis |c Jean-Pierre Aubin |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 2000 | |
| 300 | |a XVI, 495 S. | ||
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| 490 | 0 | |a Pure and applied mathematics | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface xiii
Introduction: A Guide to the Reader 1
1. The Projection Theorem 4
1.1. Definition of a Hilbert Space, 4
1.2. Review of Continuous Linear and Bilinear Operators, 10
1.3. Extension of Continuous Linear and Bilinear Operators
by Density, 13
1.4. The Best Approximation Theorem, 15
1.5. Orthogonal Projectors, 18
1.6. Closed Subspaces, Quotient Spaces, and Finite Products
of Hilbert Spaces, 22
*1.7. Orthogonal Bases for a Separable Hilbert Space, 23
2. Theorems on Extension and Separation 27
2.1. Extension of Continuous Linear and Bilinear Operators, 28
2.2. A Density Criterion, 29
2.3. Separation Theorems, 30
2.4. A Separation Theorem in Finite Dimensional Spaces, 32
2.5. Support Functions, 32
*2.6. The Duality Theorem in Convex Optimization, 34
*2.7. Von Neumann s Minimax Theorem, 39
*2.8. Characterization of Pareto Optima, 45
3. Dual Spaces and Transposed Operators 49
3.1. The Dual of a Hilbert Space, 50
3.2. Realization of the Dual of a Hilbert Space, 54
3.3. Transposition of Operators, 56
3.4. Transposition of Injective Operators, 57
vii
viii CONTENTS
3.5. Duals of Finite Products, Quotient Spaces, and Closed or
Dense Subspaces, 60
3.6. The Theorem of Lax Milgram, 64
*3.7. Variational Inequalities, 65
*3.8. Noncooperative Equilibria in w Person Quadratic
Games, 67
4. The Banach Theorem and the Banach Steinhaus Theorem 70
4.1. Properties of Bounded Sets of Operators, 71
4.2. The Mean Ergodic Theorem, 76
4.3. The Banach Theorem, 79
4.4. The Closed Range Theorem, 82
4.5. Characterization of Left Invertible Operators, 84
4.6. Characterization of Right Invertible Operators, 86
*4.7. Quadratic Programming with Linear Constraints, 90
5. Construction of Hilbert Spaces 94
5.1. The Initial Scalar Product, 96
5.2. The Final Scalar Product, 98
5.3. Normal Subspaces of a Pivot Space, 99
5.4. Minimal and Maximal Domains of a Closed Family of
Operators, 104
*5.5. Unbounded Operators and Their Adjoints, 107
*5.6. Completion of a Pre Hilbert Space Contained in a
Hilbert Space, 110
*5.7. HausdorffCompletion, 111
*5.8. The Hilbert Sum of Hilbert Spaces, 112
*5.9. Reproducing Kernels of a Hilbert Space of
Functions, 115
6. L1 Spaces and Convolution Operators 120
6.1. The Space L2(Q) of Square Integrable Functions, 121
6.2. The Spaces L2(Q, a) with Weights, 124
6.3. The Spaced, 125
6.4. The Convolution Product for Functions of ^0{W) and
of £ (« ), 128
6.5. Convolution Operators, 131
6.6. Approximation by Convolution, 133
*6.7. Example. Convolution Power for Characteristic
Functions, 135
*6.8. Example. Convolution Product for Polynomials: Appell
Polynomials, 139
CONTENTS ix
7. Sobolev Spaces of Functions of One Variable 145
7.1. The Space #om(fi) and Its Dual i/ m(Q), 146
7.2. Definition of Distributions, 148
7.3. Differentiation of Distributions, 149
7.4. Relations Between #om(Q) and H™{U), 153
7.5. The Sobolev Space Hm{Q), 154
7.6. Relations Between Hm(il) and Hm(U), 158
*7.7. Characterization of the Dual of Hm(Q.), 161
7.8. Trace Theorems, 163
7.9. Convolution of Distributions, 164
8. Some Approximation Procedures in Spaces of Functions 167
8.1. Approximation by Orthogonal Polynomials, 168
8.2. Legendre, Laguerre, and Hermite Polynomials, 170
8.3. Fourier Series, 173
8.4. Approximation by Step Functions, 175
8.5. Approximation by Piecewise Polynomial Functions, 177
8.6. Approximation in Sobolev Spaces, 183
9. Sobolev Spaces of Functions of Several Variables and the Fourier
Transform 187
9.1. The Sobolev Spaces #om(Q), Hm(Q), and H~m(Q.), 188
9.2. The Fourier Transform of Infinitely Differentiable and
Rapidly Decreasing Functions, 190
9.3. The Fourier Transform of Sobolev Spaces, 196
9.4. The Trace Theorem for the Spaces Hm(Ul), 199
9.5. The Trace Theorem for the Spaces Hm(Q.), 206
9.6. The Compactness Theorem, 209
10. Introduction to Set Valued Analysis and Convex Analysis 211
10.1. Graphical Derivations, 213
10.2. Jump Maps of Vector Distributions, 217
10.3. Epiderivatives, 222
10.4. Dual Concepts, 230
10.5. Conjugate Functions, 234
10.6. Economic Optima, 250
11. Elementary Spectral Theory 259
11.1. Compact Operators, 260
11.2. The Theory of Riesz Fredholm, 262
11.3. Characterization of Compact Operators from One
Hilbert Space to Another, 266
x CONTENTS
11.4. The Fredholm Alternative, 268
*11.5. Applications: Constructions of Intermediate Spaces, 271
*11.6. Application: Best Approximation Processes, 274
* 11.7. Perturbation of an Isomorphism by a Compact
Operator, 279
12. Hilbert Schmidt Operators and Tensor Products 283
12.1. The Hilbert Space of Hilbert Schmidt Operators, 284
12.2. The Fundamental Isomorphism Theorem, 292
12.3. Hilbert Tensor Products, 293
12.4. The Tensor Product of Continuous Linear
Operators, 298
12.5. The Hilbert Tensor Product by I2, 302
12.6. The Hilbert Tensor Product by L2, 303
12.7. The Tensor Product by the Sobolev Space Hm, 306
13. Boundary Value Problems 309
13.1. The Formal Adjoint of an Operator and Green s
Formula, 312
13.2. Green s Formula for Bilinear Forms, 321
13.3. Abstract Variational Boundary Value Problems, 327
13.4. Examples of Boundary Value Problems, 335
13.5. Approximation of Solutions to Neumann Problems, 341
13.6. Restriction and Extension of the Formal Adjoint, 346
13.7. Unilateral Boundary Value Problems, 351
13.8. Introduction to Calculus of Variations, 354
14. Differential Operational Equations and Semigroups of Operators 360
14.1. Semigroups of Operators, 362
14.2. Characterization of Infinitesimal Generators of
Semigroups, 367
14.3. Differential Operational Equations, 372
14.4. Boundary Value Problems for Parabolic Equations, 375
14.5. Systems Theory: Internal and External
Representations, 377
15. Viability Kernels and Capture Basins 385
15.1. The Nagumo Theorem, 386
15.2. Viability Kernels and Capture Basins, 399
16. First Order Partial Differential Equations 411
16.1. Some Hamilton Jacobi Equations, 414
16.2. Systems of First Order Partial Differential Equations, 428
CONTENTS xi
16.3. Lotka McKendrick Systems, 434
16.4. Distributed Boundary Data, 445
Selection of Results 448
1. General Properties, 448
2. Properties of Continuous Linear Operators, 450
3. Separation Theorems and Polarity, 451
4. Construction of Hilbert Spaces, 452
5. Compact Operators, 454
6. Semigroup of Operators, 456
7. The Green s Formula, 456
8. Set Valued Analysis and Optimization, 457
9. Convex Analysis, 459
10. Minimax Inequalities, 463
11. Sobolev Spaces, Convolution, and Fourier Transform, 463
12. Viability Kernels and Capture Basins, 465
13. First Order Partial Differential Equations, 467
Exercises 470
Bibliography 488
Index 493
|
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| indexdate | 2024-07-09T18:38:06Z |
| institution | BVB |
| isbn | 0471179760 |
| language | English |
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| physical | XVI, 495 S. |
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| spelling | Aubin, Jean-Pierre Verfasser aut Applied functional analysis Jean-Pierre Aubin 2. ed. New York [u.a.] Wiley 2000 XVI, 495 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Aus dem Franz. übers. Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Hilbert-Raum (DE-588)4159850-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008884111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aubin, Jean-Pierre Applied functional analysis Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4018916-8 |
| title | Applied functional analysis |
| title_auth | Applied functional analysis |
| title_exact_search | Applied functional analysis |
| title_full | Applied functional analysis Jean-Pierre Aubin |
| title_fullStr | Applied functional analysis Jean-Pierre Aubin |
| title_full_unstemmed | Applied functional analysis Jean-Pierre Aubin |
| title_short | Applied functional analysis |
| title_sort | applied functional analysis |
| topic | Functional analysis Hilbert space Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Hilbert space Hilbert-Raum Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008884111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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