Linear integral equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
|
| Edition: | 2. ed. |
| Series: | Applied mathematical sciences
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 365 Seiten Illustrationen |
| ISBN: | 0387987002 |
Staff View
MARC
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| 100 | 1 | |a Kress, Rainer |d 1941- |e Verfasser |0 (DE-588)115774416 |4 aut | |
| 245 | 1 | 0 | |a Linear integral equations |c Rainer Kress |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1999 | |
| 300 | |a XIV, 365 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 82 | |
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition ix
1 Normed Spaces 1
1.1 Convergence and Continuity 2
1.2 Completeness 5
1.3 Compactness 6
1.4 Scalar Products 9
1.5 Best Approximation 11
Problems 13
2 Bounded and Compact Operators 15
2.1 Bounded Operators 15
2.2 Integral Operators 17
2.3 Neumann Series 18
2.4 Compact Operators 20
Problems 27
3 Riesz Theory 28
3.1 Riesz Theory for Compact Operators 28
3.2 Spectral Theory for Compact Operators 34
3.3 Volterra Integral Equations 36
Problems 38
xii Contents
4 Dual Systems and Fredholm Alternative 39
4.1 Dual Systems via Bilinear Forms 39
4.2 Dual Systems via Sesquilinear Forms 41
4.3 The Fredholm Alternative 45
4.4 Boundary Value Problems 50
Problems 53
5 Regularization in Dual Systems 55
5.1 Regularizers 55
5.2 Normal Solvability 57
5.3 Index 62
Problems 66
6 Potential Theory 67
6.1 Harmonic Functions 67
6.2 Boundary Value Problems: Uniqueness 74
6.3 Surface Potentials 78
6.4 Boundary Value Problems: Existence 82
6.5 Nonsmooth Boundaries 87
Problems 92
7 Singular Integral Equations 94
7.1 Holder Continuity 94
7.2 The Cauchy Integral Operator 97
7.3 The Riemann Problem 105
7.4 Integral Equations with Cauchy Kernel 107
7.5 Cauchy Integral and Logarithmic Potential 115
7.6 Logarithmic Single Layer Potential on an Arc 120
Problems 124
8 Sobolev Spaces 125
8.1 The Sobolev Space Hp[0,2w] 125
8.2 The Sobolev Space HP(T) 135
8.3 Weak Solutions to Boundary Value Problems 142
Problems 151
9 The Heat Equation 152
9.1 Initial Boundary Value Problem: Uniqueness 152
9.2 Heat Potentials 155
9.3 Initial Boundary Value Problem: Existence 160
Problems 162
10 Operator Approximations 163
10.1 Approximations via Norm Convergence 164
10.2 Uniform Boundedness Principle 165
Contents xiii
10.3 Collectively Compact Operators 167
10.4 Approximations via Pointwise Convergence 168
10.5 Successive Approximations 170
Problems 175
11 Degenerate Kernel Approximation 177
11.1 Degenerate Operators and Kernels 178
11.2 Interpolation 179
11.3 Trigonometric Interpolation 182
11.4 Degenerate Kernels via Interpolation 187
11.5 Degenerate Kernels via Expansions 192
Problems 195
12 Quadrature Methods 197
12.1 Numerical Integration 198
12.2 Nystrom s Method 201
12.3 Weakly Singular Kernels 206
12.4 Nystrom s Method in Sobolev Spaces 213
Problems 216
13 Projection Methods 218
13.1 The Projection Method 218
13.2 Projection Methods for Equations of the Second Kind . . . 223
13.3 The Collocation Method 225
13.4 Collocation Methods for Equations of the First Kind .... 232
13.5 The Galerkin Method 240
Problems 245
14 Iterative Solution and Stability 247
14.1 Stability of Linear Systems 248
14.2 Two Grid Methods 251
14.3 Multigrid Methods 255
14.4 Fast Matrix Vector Multiplication 260
Problems 264
15 Equations of the First Kind 265
15.1 Ill Posed Problems 265
15.2 Regularization of Ill Posed Problems 269
15.3 Compact Self Adjoint Operators 271
15.4 Singular Value Decomposition 277
15.5 Regularization Schemes 281
Problems 289
16 Tikhonov Regularization 290
16.1 The Tikhonov Functional 290
xiv Contents
16.2 Weak Convergence 291
16.3 Quasi Solutions 292
16.4 Minimum Norm Solutions 298
16.5 Classical Tikhonov Regularization 301
Problems 307
17 Regularization by Discretization 308
17.1 Projection Methods for Ill Posed Equations 308
17.2 The Moment Method 313
17.3 Hilbert Spaces with Reproducing Kernel 315
17.4 Moment Collocation 317
Problems 318
18 Inverse Boundary Value Problems 320
18.1 Ill Posed Equations in Potential Theory 320
18.2 An Inverse Problem in Potential Theory 328
18.3 Approximate Solution via Potentials 333
18.4 Differentiability with Respect to the Boundary 341
Problems 345
References 347
Index 361
|
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| callnumber-sort | QA 11 _Q A431 A647 VOL 282 41999 |
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| discipline | Mathematik |
| edition | 2. ed. |
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| id | DE-604.BV012477091 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:28:16Z |
| institution | BVB |
| isbn | 0387987002 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008468529 |
| oclc_num | 246340344 |
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| owner_facet | DE-20 DE-703 DE-355 DE-BY-UBR DE-29T DE-91G DE-BY-TUM DE-521 DE-634 DE-83 DE-188 |
| physical | XIV, 365 Seiten Illustrationen |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Kress, Rainer 1941- Verfasser (DE-588)115774416 aut Linear integral equations Rainer Kress 2. ed. New York [u.a.] Springer 1999 XIV, 365 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 82 Lineare Integralgleichung - Lehrbuch Integral equations Lineare Integralgleichung (DE-588)4114426-0 gnd rswk-swf Lineare Integralgleichung (DE-588)4114426-0 s DE-604 Applied mathematical sciences 82 (DE-604)BV000005274 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008468529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kress, Rainer 1941- Linear integral equations Applied mathematical sciences Lineare Integralgleichung - Lehrbuch Integral equations Lineare Integralgleichung (DE-588)4114426-0 gnd |
| subject_GND | (DE-588)4114426-0 |
| title | Linear integral equations |
| title_auth | Linear integral equations |
| title_exact_search | Linear integral equations |
| title_full | Linear integral equations Rainer Kress |
| title_fullStr | Linear integral equations Rainer Kress |
| title_full_unstemmed | Linear integral equations Rainer Kress |
| title_short | Linear integral equations |
| title_sort | linear integral equations |
| topic | Lineare Integralgleichung - Lehrbuch Integral equations Lineare Integralgleichung (DE-588)4114426-0 gnd |
| topic_facet | Lineare Integralgleichung - Lehrbuch Integral equations Lineare Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008468529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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