Matricial version of the classical Schur problem:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Stuttgart u.a.
Teubner
1992
|
| Series: | Teubner-Texte zur Mathematik
129 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 355 S. |
| ISBN: | 3815420156 |
Staff View
MARC
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| 100 | 1 | |a Dubovoj, Vladimir K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Matricial version of the classical Schur problem |c Vladimir K. Dubovoj ; Bernd Fritzsche ; Bernd Kirstein |
| 264 | 1 | |a Stuttgart u.a. |b Teubner |c 1992 | |
| 300 | |a 355 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Teubner-Texte zur Mathematik |v 129 | |
| 650 | 7 | |a Interpolation |2 ram | |
| 650 | 7 | |a Matrices |2 ram | |
| 650 | 4 | |a algorithme Schur | |
| 650 | 4 | |a interpolation | |
| 650 | 4 | |a inégalité matricielle | |
| 650 | 4 | |a problème Schur | |
| 650 | 4 | |a Interpolation | |
| 650 | 4 | |a Matrices | |
| 650 | 0 | 7 | |a Schur-Analysis |0 (DE-588)4281622-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schur-Funktion |0 (DE-588)4180243-3 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Fritzsche, Bernd |e Verfasser |4 aut | |
| 700 | 1 | |a Kirstein, Bernd |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804118832174858240 |
|---|---|
| adam_text | CONTENTS
0. Notation and preliminaries 8
Chapter 1 Basic algebraic concepts 13
1.1. Matrix formulas 13
1.2. Some facts on matrix polynomials 24
1.3. Some basic facts from J algebra 26
1.4. On J modulus 37
1.5. Matrix balls 44
1.6. Linear fractional transformations of matrices 52
1.7. Notes and comments 59
Chapter 2 Matrix valued Schur and Caratheodory functions 60
2.1. Elementary properties of matrix valued Schur and
Caratheodory functions 60
2.2. Herglotz Bochner s Theorem and F. Riesz Herglotz
Theorem 65
2.3. Schwarz Pick inequalities for matrix valued
Caratheodory and Schur functions 72
2.4. The Potapov class of matrix valued functions 77
2.5. S. A. Orlov s Theorem 87
2.6. Notes and comments 108
Chapter 3 An approach to the matricial Schur problem based
on the Schur Potapov algorithm 109
3.1. Characterizing matrix valued functions by their Taylor
coefficients 109
3.2. Completion of non negative Hermitian block matrices 114
3.3. Completion of contractions 119
3.4. The coefficient problem for matrix valued Caratheodory
functions 122
3.5. The coefficient problem for matrix valued Schur
functions 125
3.6. Orthogonal matrix polynomials corresponding to a non
negative Hermitian Borel measure on the unit circle 132
3.7. Schur systems of matrix polynomials 173
3.8. The Schur Potapov Algorithm 179
3.9. The matricial version of the classical Schur problem 191
3.10. Connections to the Arov Krein approach 194
3.11. On the Weyl limit semi radii of a Schur function 200
3.12. Notes and comments 203
6
Chapter 4 J elementary factors 205
4.1. Fundamental matrix inequalities of splitting off 205
4.2. Notion and first properties of J elementary factors 215
4.3. splitting off of J elementary factors 226
4.4. Parametrization of full rank J elementary factors 234
4.5. Notes and comments 252
Chapter 5 The matricial Schur problem and J contractive
matrix valued functions 252
5.1. Necessary and sufficient conditions for solvability
of the matricial Schur problem 253
5.2. Fundamental matrix inequalities associated with the
Schur problem 258
5.3. Solution of the fundamental matrix inequalities 267
5.4. Solution of the Schur problem step by step 271
5.5. Weyl matrix balls connected with the matricial Schur
problem 290
5.6. Defect numbers of a matricial Schur function 317
5.7. Notes and comments 328
References 330
Index 352
7
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| any_adam_object | 1 |
| author | Dubovoj, Vladimir K. Fritzsche, Bernd Kirstein, Bernd |
| author_facet | Dubovoj, Vladimir K. Fritzsche, Bernd Kirstein, Bernd |
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| dewey-full | 511/.42 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.42 |
| dewey-search | 511/.42 |
| dewey-sort | 3511 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV004715433 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:16:33Z |
| institution | BVB |
| isbn | 3815420156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002897399 |
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| physical | 355 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Teubner |
| record_format | marc |
| series | Teubner-Texte zur Mathematik |
| series2 | Teubner-Texte zur Mathematik |
| spelling | Dubovoj, Vladimir K. Verfasser aut Matricial version of the classical Schur problem Vladimir K. Dubovoj ; Bernd Fritzsche ; Bernd Kirstein Stuttgart u.a. Teubner 1992 355 S. txt rdacontent n rdamedia nc rdacarrier Teubner-Texte zur Mathematik 129 Interpolation ram Matrices ram algorithme Schur interpolation inégalité matricielle problème Schur Interpolation Matrices Schur-Analysis (DE-588)4281622-1 gnd rswk-swf Schur-Funktion (DE-588)4180243-3 gnd rswk-swf Matrizenanalysis (DE-588)4227735-8 gnd rswk-swf Schur-Analysis (DE-588)4281622-1 s DE-604 Schur-Funktion (DE-588)4180243-3 s Matrizenanalysis (DE-588)4227735-8 s Fritzsche, Bernd Verfasser aut Kirstein, Bernd Verfasser aut Teubner-Texte zur Mathematik 129 (DE-604)BV000012607 129 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002897399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dubovoj, Vladimir K. Fritzsche, Bernd Kirstein, Bernd Matricial version of the classical Schur problem Teubner-Texte zur Mathematik Interpolation ram Matrices ram algorithme Schur interpolation inégalité matricielle problème Schur Interpolation Matrices Schur-Analysis (DE-588)4281622-1 gnd Schur-Funktion (DE-588)4180243-3 gnd Matrizenanalysis (DE-588)4227735-8 gnd |
| subject_GND | (DE-588)4281622-1 (DE-588)4180243-3 (DE-588)4227735-8 |
| title | Matricial version of the classical Schur problem |
| title_auth | Matricial version of the classical Schur problem |
| title_exact_search | Matricial version of the classical Schur problem |
| title_full | Matricial version of the classical Schur problem Vladimir K. Dubovoj ; Bernd Fritzsche ; Bernd Kirstein |
| title_fullStr | Matricial version of the classical Schur problem Vladimir K. Dubovoj ; Bernd Fritzsche ; Bernd Kirstein |
| title_full_unstemmed | Matricial version of the classical Schur problem Vladimir K. Dubovoj ; Bernd Fritzsche ; Bernd Kirstein |
| title_short | Matricial version of the classical Schur problem |
| title_sort | matricial version of the classical schur problem |
| topic | Interpolation ram Matrices ram algorithme Schur interpolation inégalité matricielle problème Schur Interpolation Matrices Schur-Analysis (DE-588)4281622-1 gnd Schur-Funktion (DE-588)4180243-3 gnd Matrizenanalysis (DE-588)4227735-8 gnd |
| topic_facet | Interpolation Matrices algorithme Schur interpolation inégalité matricielle problème Schur Schur-Analysis Schur-Funktion Matrizenanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002897399&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012607 |
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