Approximation of additive convolution-like operators: real C*-algebra approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2008
|
| Series: | Frontiers in mathematics
|
| Subjects: | |
| Links: | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2467209&custom_att_2=simple_viewer http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016741211&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XII, 306 S. graph. Darst. |
| ISBN: | 9783764387501 |
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MARC
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| 245 | 1 | 0 | |a Approximation of additive convolution-like operators |b real C*-algebra approach |c Victor D. Didenko ; Bernd Silbermann |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2008 | |
| 300 | |a XII, 306 S. |b graph. Darst. | ||
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| 490 | 0 | |a Frontiers in mathematics | |
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Record in the Search Index
| _version_ | 1819362079126061056 |
|---|---|
| adam_text | Contents
Preface
ix
1
Complex
and Real Algebras
1
1.1
Complex and Real C*-Algebras
.................... 1
1.2
Real Extensions of Complex
*-
Algebras
............... 4
1.3
Uniqueness of Involution in Real Extensions of Complex -Algebras
7
1.4
Real and Complex Spectrum. Inverse Closedness
.......... 15
1.5
Moore-Penrose Invertibility in Algebra
Λ
.............. 20
1.6
Operator Sequences: Stability
..................... 24
1.7
Asymptotic Moore-Penrose Invertibility
............... 31
1.8
Approximation Methods in Para-Algebras
.............. 38
1.9
Local Principles
............................. 41
1.9.1
Gohberg-Krupnik Local Principle
............... 41
1.9.2
Allan s Local Principle
.................... 44
1.9.3
Local Principle for Para-algebras
............... 45
1.10
Singular Integral and Mellin Operators
............... 47
1.10.1
Singular Integrals
........................ 47
1.10.2
The Algebra
ΣΡ(α)
..................... 49
1.10.3
Integral Representations
.................... 51
1.10.4
The Algebra
ΣΡ(α, β, ν)
................... 52
1.10.5
Singular Integral Operators with Piecewise Continuous
Coefficients
........................... 53
1.10.6
Singular Integral Operators with Conjugation
........ 56
1.11
Comments and References
....................... 57
2
Integral Operators. Smooth Curves
59
2.1
Polynomial Galerkin Method
..................... 60
2.2
Polynomial Collocation Method
.................... 65
2.3
Equations with Differential Operators
................ 69
2.3.1
Singular Integro-Differential Equations
............ 69
2.3.2
Approximate Solution of Singular Integro-Differential
Equations with Conjugation
.................. 72
. Contents
2.4
A
C*-Algebra
of
Operator
Sequences
................
73
2.4.1 Moore-Penrose Invertibility..................
86
2.5
The e-Collocation Method
.......................
86
2.6
Spline Galerkin Method
........................
91
2.7
Quadrature Methods on the Unit Circle
...............
93
2.8
Polynomial Qualocation Method
...................
Ю0
2.9
Spline Qualocation Method
......................
Ю4
2.10
Quadrature Methods on Closed Smooth Curves
...........
ИЗ
2.11
A Remark on Tensor Product Techniques
..............
П7
2.12
Comments and References
.......................
П9
3
Riemann-Hilbert Problem 123
3.1
Galerkin Method
............................
123
3.2
Interpolation Method. Continuous Coefficients
........... 131
3.3
Local Principle for the Para-Algebra
Л/
J
..............
136
3.4
Discontinuous Coefficients
....................... 14
3.5
Generalized
Riemann-Hilbert-Poincaré
Problem
........... 152
3.6
Comments and References
....................... 154
4
Piecewise Smooth and Open Contours
^
4.1
Stability of Approximation Methods
................. 15
4.1.1
Quadrature Methods for Singular Integral Equations with
Conjugation
........................... 15°
4.1.2
The g-Collocation Method
...................
168
4.1.3
Qualocation Method
......................
ł7°
4.2
Fredholm
Properties of Local Operators
............... 1^1
4.2.1
Quadrature Methods
...................... 172
4.2.2
The e-Collocation Method
...................
176
4.2.3
Qualocation Method
......................
I?9
4.3
La-Spaces with Weight
.........................
I80
4.3.1
A Quadrature Method and Its Stability
...........
I80
4.3.2
Local Operators and Their Indices
..............
l8^
4.3.3
The Vanishing of the Index of Local Operators
.......
l9^
4.3.4
Modification of the Quadrature Method by Cutting Off
Corner Singularities
...................... 1
4.4
Double Layer Potential Equation
................... 202
4.4.1
Quadrature Methods
...................... 203
4.4.2
The e-Collocation Method
................... 206
4.4.3
Qualocation Method
...................... 207
4.5
Mellin Operators with Conjugation
.................. 208
4.5.1
A Quadrature Method
..................... 210
4.5.2
Predholm Properties of Local Operators
........... 213
4.5.3
Index of the Local Operators
................. 218
4.5.4
Examples of the Essential Spectrum of Local Operators
. ■ 226
Contents
vii
4.6
Comments and References
....................... 230
5
Muskhelishvili Equation
233
5.1
Boundary Problems for the Biharmonic Equation
.......... 233
5.1.1
Reduction of Biharmonic Problems to a Boundary Problem
for Two Analytic Functions
.................. 234
5.1.2
Reduction of Boundary Problems for Two Analytic
Functions to Integral Equations
................ 241
5.2
Fredholm
Properties. Invertibility
................... 244
5.3
Approximations on Smooth Contours
................. 256
5.3.1
Galerkin Method
........................ 257
5.3.2
The e-Collocation Method
................... 259
5.3.3
Qualocation Method
...................... 261
5.3.4
Biharmonic Problem
...................... 262
5.4
Approximation Methods on Special Contours
............ 265
5.5
Galerkin Method. Piecewise Smooth Contour
............ 270
5.6
Comments and References
....................... 272
6
Numerical Examples
275
6.1
Muskhelishvili Equation
........................ 275
6.2
Biharmonic Problem
.......................... 281
Bibliography
285
Index
303
|
| any_adam_object | 1 |
| author | Didenko, Victor D. Silbermann, Bernd 1941- |
| author_GND | (DE-588)124151035 |
| author_facet | Didenko, Victor D. Silbermann, Bernd 1941- |
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| author_sort | Didenko, Victor D. |
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| ctrlnum | (OCoLC)254723483 (DE-599)HBZHT015547354 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035072839 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:19:29Z |
| institution | BVB |
| isbn | 9783764387501 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016741211 |
| oclc_num | 254723483 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-824 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-824 |
| physical | XII, 306 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Frontiers in mathematics |
| spellingShingle | Didenko, Victor D. Silbermann, Bernd 1941- Approximation of additive convolution-like operators real C*-algebra approach C*-algebras Convolutions (Mathematics) Additiver Operator (DE-588)4401251-2 gnd C-Stern-Algebra (DE-588)4136693-1 gnd Faltungsoperator (DE-588)4388315-1 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4401251-2 (DE-588)4136693-1 (DE-588)4388315-1 (DE-588)4002498-2 |
| title | Approximation of additive convolution-like operators real C*-algebra approach |
| title_auth | Approximation of additive convolution-like operators real C*-algebra approach |
| title_exact_search | Approximation of additive convolution-like operators real C*-algebra approach |
| title_full | Approximation of additive convolution-like operators real C*-algebra approach Victor D. Didenko ; Bernd Silbermann |
| title_fullStr | Approximation of additive convolution-like operators real C*-algebra approach Victor D. Didenko ; Bernd Silbermann |
| title_full_unstemmed | Approximation of additive convolution-like operators real C*-algebra approach Victor D. Didenko ; Bernd Silbermann |
| title_short | Approximation of additive convolution-like operators |
| title_sort | approximation of additive convolution like operators real c algebra approach |
| title_sub | real C*-algebra approach |
| topic | C*-algebras Convolutions (Mathematics) Additiver Operator (DE-588)4401251-2 gnd C-Stern-Algebra (DE-588)4136693-1 gnd Faltungsoperator (DE-588)4388315-1 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | C*-algebras Convolutions (Mathematics) Additiver Operator C-Stern-Algebra Faltungsoperator Approximation |
| url | http://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2467209&custom_att_2=simple_viewer http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016741211&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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