Toeplitz matrices, asymptotic linear algebra, and functional analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2000
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008894502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | X, 116 S. |
| ISBN: | 3764362901 |
Staff View
MARC
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| 100 | 1 | |a Böttcher, Albrecht |d 1954- |e Verfasser |0 (DE-588)110234979 |4 aut | |
| 245 | 1 | 0 | |a Toeplitz matrices, asymptotic linear algebra, and functional analysis |c Albrecht Böttcher ; Sergei M. Grudsky |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2000 | |
| 300 | |a X, 116 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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| 650 | 7 | |a C*-algèbres |2 ram | |
| 650 | 7 | |a Toeplitz, Matrices de |2 ram | |
| 650 | 4 | |a C*-algebras | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Toeplitz matrices | |
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| 650 | 0 | 7 | |a Funktionalanalysis |0 (DE-588)4018916-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Toeplitz-Matrix |0 (DE-588)4185611-9 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008894502 | |
Record in the Search Index
| DE-BY-TUM_call_number | 0202 MAT 467f 2004 A 128 |
|---|---|
| DE-BY-TUM_katkey | 1478030 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020743031 |
| _version_ | 1821933065896722432 |
| adam_text | Contents
Preface
vii
1
Infinite Toeplitz
Matrices
1
1.1
Boundedness
....................... 1
1.2
Compactness and
Selfadjointness
............ 3
1.3
C-Algebras
........................ 4
1.4
Fredholm Operators...................
6
1.5
Continuous Symbols
................... 8
1.6
Notes
. . ......................... 13
2
С*-
Algebras in Action
14
2.1
Finite Section Method
.................. 14
2.2
Perturbed Toeplitz Matrices
............... 16
2.3
Algebraization of Stability
................ 18
2.4
Stability Criteria
..................... 21
2.5
Asymptotic Inverses
................... 23
2.6
Norms
........................... 24
2.7
Norms of Inverses
..................... 24
2.8
Condition Numbers
.................... 25
2.9
Eigenvalues of Hermitian Matrices
........... 26
2.10
Singular Values
...................... 28
2.11
Pseudospectra
....................... 30
2.12
Notes
........................... 33
3
Instability
36
3.1
Some Standard Tricks
.................. 36
3.2
At Least Polynomial Growth
.............. 38
3.3
At Most Polynomial Growth
............... 41
3.4
Semi-Definite Hermitian
Matricos
............ 46
vi
Contents
3.5
Exponential Growth
................... 47
3.6
Notes
........................... 49
4
Condition Numbers
52
4.1
Norms of Pure Toeplitz Matrices
............ 52
4.2
Structure of the Inverse
................. 56
4.3
Perturbed Toeplitz Band Matrices
........... 58
4.4
Norms of the Inverses of Toeplitz Matrices
....... 67
4.5
Condition Numbers of Toeplitz Matrices
........ 73
4.6
Condition Numbers of Toeplitz-Like Matrices
..... 75
4.7
Notes
........................... 77
5
Singular Values
78
5.1
Basic Facts
........................ 78
5.2
The Splitting Phenomenon
............... 80
5.3
Extreme Singular Values
................. 84
5.4
The First
Szegő
Limit Theorem
............. 88
5.5
The Avram-Parter Theorem
............... 92
5.6
Circulants
......................... 94
5.7
Ţoeplitz
Band Matrices
................. 97
5.8
Zizler, Zuidwijk, Taylor, Arimoto
............ 98
5.9
Notes
........................... 104
Bibliography
107
Notation Index
113
Subject Index
115
|
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| author | Böttcher, Albrecht 1954- Grudskij, Sergej M. |
| author_GND | (DE-588)110234979 |
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| classification_rvk | SK 600 SK 620 |
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| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013053141 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:40:39Z |
| institution | BVB |
| isbn | 3764362901 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008894502 |
| oclc_num | 43567651 |
| open_access_boolean | |
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| physical | X, 116 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Birkhäuser |
| record_format | marc |
| spellingShingle | Böttcher, Albrecht 1954- Grudskij, Sergej M. Toeplitz matrices, asymptotic linear algebra, and functional analysis Analyse fonctionnelle ram C*-algèbres ram Toeplitz, Matrices de ram C*-algebras Functional analysis Toeplitz matrices C-Stern-Algebra (DE-588)4136693-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd Toeplitz-Matrix (DE-588)4185611-9 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4018916-8 (DE-588)4185611-9 |
| title | Toeplitz matrices, asymptotic linear algebra, and functional analysis |
| title_auth | Toeplitz matrices, asymptotic linear algebra, and functional analysis |
| title_exact_search | Toeplitz matrices, asymptotic linear algebra, and functional analysis |
| title_full | Toeplitz matrices, asymptotic linear algebra, and functional analysis Albrecht Böttcher ; Sergei M. Grudsky |
| title_fullStr | Toeplitz matrices, asymptotic linear algebra, and functional analysis Albrecht Böttcher ; Sergei M. Grudsky |
| title_full_unstemmed | Toeplitz matrices, asymptotic linear algebra, and functional analysis Albrecht Böttcher ; Sergei M. Grudsky |
| title_short | Toeplitz matrices, asymptotic linear algebra, and functional analysis |
| title_sort | toeplitz matrices asymptotic linear algebra and functional analysis |
| topic | Analyse fonctionnelle ram C*-algèbres ram Toeplitz, Matrices de ram C*-algebras Functional analysis Toeplitz matrices C-Stern-Algebra (DE-588)4136693-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd Toeplitz-Matrix (DE-588)4185611-9 gnd |
| topic_facet | Analyse fonctionnelle C*-algèbres Toeplitz, Matrices de C*-algebras Functional analysis Toeplitz matrices C-Stern-Algebra Funktionalanalysis Toeplitz-Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008894502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bottcheralbrecht toeplitzmatricesasymptoticlinearalgebraandfunctionalanalysis AT grudskijsergejm toeplitzmatricesasymptoticlinearalgebraandfunctionalanalysis |
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| Call Number: |
0202 MAT 467f 2004 A 128
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