Invertibility and asymptotics of Toeplitz matrices:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Akad.-Verl.
1983
|
| Series: | Mathematical research
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 200 S. |
| ISSN: | 0138-3019 |
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 Invertibility and asymptotics of Toeplitz matrices |c by Albrecht Böttcher and Bernd Silbermann |
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1983 | |
| 300 | |a 200 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematical research |v 17 |x 0138-3019 | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Silbermann, Bernd |d 1941- |e Verfasser |0 (DE-588)124151035 |4 aut | |
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Record in the Search Index
| _version_ | 1804114692210163712 |
|---|---|
| adam_text | CONTENTS
CHAPTER 1. SOME FACTS FROM FUNCTIONAL ANALYSIS 9
Operator ideals 9
Operator determinants 12
Fredholm operators 14
A local principle 16
Operator matrices and their determinants 17
Functions on the unit circle 18
Notes and comments 21
CHAPTER 2. TOEPLITZ OPERATORS 23
Definition of Toeplitz and Hankel operators 23
LM symbols 25
C + H20 symbols 31
Continuous symbols 33
Piecewise continuous symbols 35
Matrix symbols 42
Algebras generated by Toeplitz operators 48
Notes and comments 53
CHAPTER 3. THE FINITE SECTION MBTHOD 56
Projection methods 56
The finite section method 58
Constructive theory 61
Local theory 66
Notes and comments 74
(with some information about Wiener Hopf integral
operators, two dimensi6nal Toeplitz and Wiener Hopf
operators, and effective inversion of finite Toeplitz
matrices)
CHAPTER 4. SOME BANACH ALGEBRAS RELATED WITH OPERATOR IDEALS 86
Banach algebras generated by ideals 86
Banach algebras generated by Hankel operators 92
A generalization of the algebras ^P 1/q 94
Notes and comments 102
7
CHAPTER 5. FACTORIZATION IN ALGEBRAS OF ESSENTIALLY BOUNDED
MATRIX FUNCTIONS 103
Formulation of the main result 103
Proof of necessity 105
Canonical factorization 106
Proof of sufficiency 108
Decomposing algebras with factorization property 114
Notes and comments 118
CHAPTER 6. TOEPLITZ DETERMINANTS 120
The terms G(a) and E(a) 120
The Strong SzegS Limit Theorem 126
The effect of smoothness 129
Nonvanishing index 139
Semirational generating functions 141
Rational generating functions 145
Self adjoint generating functions 150
Pieeewise continuous generating functions 155
Notes and comments 165
(with some information about the asymptotic distribution of
eigenvalues, continuous analogues and higher dimensional
versions of Szego1s limit theorem)
CHAPTER 7. SINGULAR GENERATING FUNCTIONS 173
The conjecture of Fisher and Hartwig 173
Special cases 174
Separation of disjoint singularities 177
Notes and comments 185
REFERENCES 186
NOTATION INDEX 197
SUBJECT INDEX 199
8
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| any_adam_object | 1 |
| author | Böttcher, Albrecht 1954- Silbermann, Bernd 1941- |
| author_GND | (DE-588)110234979 (DE-588)124151035 |
| author_facet | Böttcher, Albrecht 1954- Silbermann, Bernd 1941- |
| author_role | aut aut |
| author_sort | Böttcher, Albrecht 1954- |
| author_variant | a b ab b s bs |
| building | Verbundindex |
| bvnumber | BV000229238 |
| classification_rvk | SK 220 SK 470 SK 620 |
| ctrlnum | (OCoLC)230630178 (DE-599)BVBBV000229238 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000229238 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:45Z |
| institution | BVB |
| issn | 0138-3019 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000137291 |
| oclc_num | 230630178 |
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| physical | 200 S. |
| psigel | TUB-www |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Böttcher, Albrecht 1954- Verfasser (DE-588)110234979 aut Invertibility and asymptotics of Toeplitz matrices by Albrecht Böttcher and Bernd Silbermann Berlin Akad.-Verl. 1983 200 S. txt rdacontent n rdamedia nc rdacarrier Mathematical research 17 0138-3019 Toeplitz-Operator (DE-588)4191521-5 gnd rswk-swf Toeplitz-Matrix (DE-588)4185611-9 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Toeplitz-Matrix (DE-588)4185611-9 s Asymptotik (DE-588)4126634-1 s Toeplitz-Operator (DE-588)4191521-5 s DE-604 Silbermann, Bernd 1941- Verfasser (DE-588)124151035 aut Mathematical research 17 (DE-604)BV000008585 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Böttcher, Albrecht 1954- Silbermann, Bernd 1941- Invertibility and asymptotics of Toeplitz matrices Mathematical research Toeplitz-Operator (DE-588)4191521-5 gnd Toeplitz-Matrix (DE-588)4185611-9 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4191521-5 (DE-588)4185611-9 (DE-588)4126634-1 |
| title | Invertibility and asymptotics of Toeplitz matrices |
| title_auth | Invertibility and asymptotics of Toeplitz matrices |
| title_exact_search | Invertibility and asymptotics of Toeplitz matrices |
| title_full | Invertibility and asymptotics of Toeplitz matrices by Albrecht Böttcher and Bernd Silbermann |
| title_fullStr | Invertibility and asymptotics of Toeplitz matrices by Albrecht Böttcher and Bernd Silbermann |
| title_full_unstemmed | Invertibility and asymptotics of Toeplitz matrices by Albrecht Böttcher and Bernd Silbermann |
| title_short | Invertibility and asymptotics of Toeplitz matrices |
| title_sort | invertibility and asymptotics of toeplitz matrices |
| topic | Toeplitz-Operator (DE-588)4191521-5 gnd Toeplitz-Matrix (DE-588)4185611-9 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Toeplitz-Operator Toeplitz-Matrix Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000137291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT bottcheralbrecht invertibilityandasymptoticsoftoeplitzmatrices AT silbermannbernd invertibilityandasymptoticsoftoeplitzmatrices |