Metric constrained interpolation, commutant lifting and systems:
Saved in:
| Format: | Book |
|---|---|
| Language: | German |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
1998
|
| Series: | Operator theory
100 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 561 - 573 |
| Physical Description: | XII, 587 S. |
| ISBN: | 3764358890 0817658890 |
Staff View
MARC
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| 245 | 1 | 0 | |a Metric constrained interpolation, commutant lifting and systems |c C. Foias ... |
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| 500 | |a Literaturverz. S. 561 - 573 | ||
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| 650 | 4 | |a Lifting theory | |
| 650 | 4 | |a State-space methods | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Page
PREFACE v
TABLE OF CONTENTS vii
INTRODUCTION 1
PART A INTERPOLATION AND TIME INVARIANT SYSTEMS 7
I. INTERPOLATION PROBLEMS FOR OPERATOR VALUED FUNCTIONS 9
1.1. PRELIMINARIES ABOUT NOTATION AND TERMINOLOGY 9
1.2. NEVANLINNA PICK INTERPOLATION 15
1.3. TANGENTIAL NEVANLINNA PICK INTERPOLATION 17
1.4. CONTROLLABILITY OPERATORS AND INTERPOLATION 20
1.5. TANGENTIAL HERMITE FEJER INTERPOLATION 22
1.6. THE NEHARI EXTENSION PROBLEM 30
1.7. SARASON INTERPOLATION 33
1.8. NEVANLINNA PICK INTERPOLATION VIEWED AS A SARASON
PROBLEM 35
1.9. TWO SIDED NUDELMAN INTERPOLATION 38
1.10. THE TWO SIDED SARASON PROBLEM 40
1.11. A FILTERING PROBLEM 42
NOTES TO CHAPTER 1 49
II. PROOFS USING THE COMMUTANT LIFTING THEOREM 51
ILL THE COMMUTANT LIFTING THEOREM 51
11.2. PROOF OF THE STANDARD LEFT NEVANLINNA PICK
INTERPOLATION THEOREM 55
11.3. PROOF OF THE NEHARI EXTENSION THEOREM 56
viii TABLE OF CONTENTS
11.4. PROOF OF THE SARASON THEOREM 59
11.5. PROOF OF THE TWO SIDED NUDELMAN THEOREM 60
11.6. PROOF OF THE TWO SIDED SARASON THEOREM 69
NOTES TO CHAPTER II 71
III. TIME INVARIANT SYSTEMS 73
111.1. STATE SPACE ANALYSIS 73
111.2. CONTROLLABILITY AND OBSERVABILITY 76
111.3. POINT EVALUATION 83
111.4. REALIZATION THEORY 86
111.5. ANTICAUSAL REALIZATIONS 94
111.6. COMPUTING THE HANKEL FORM 99
111.7. COMPUTING THE PROJECTION IN THE SARASON PROBLEM 102
111.8. EXPLICIT CONVERSION FORMULAS 113
111.9. CONNECTING NUDELMAN AND TWO SIDED SARASON
PROBLEMS 116
III. 10. ISOMETRIC AND UNITARY SYSTEMS 122
NOTES TO CHAPTER III 130
IV. CENTRAL COMMUTANT LIFTING 131
IV. 1. MINIMAL ISOMETRIC LIFTINGS 131
IV.2. THE CENTRAL INTERTWINING LIFTING 135
IV.3. CENTRAL INTERTWINING LIFTING FORMULAS 145
IV.4. CENTRAL INTERTWINING LIFTING QUOTIENT FORMULAS 148
IV.5. THE CENTRAL SCHUR SOLUTION 154
IV.6. THE QUASI OUTER FACTOR FOR D|y 159
IV.7. MAXIMUM ENTROPY 168
IV.8. SOME MIXED BOUNDS FOR THE CENTRAL INTERTWINING
LIFTING 179
IV.9. A MIXED TWO SIDED SARASON RESULT 185
NOTES TO CHAPTER IV 190
TABLE OF CONTENTS ix
V. CENTRAL STATE SPACE SOLUTIONS 191
V.I. THE CENTRAL FORMULA FOR NEVANLINNA PICK 191
V.2. CENTRAL NEVANLINNA PICK SOLUTIONS 203
V.3. THE CENTRAL HERMITE FEJER SOLUTION 206
V.4. THE CENTRAL FORMULA FOR THE SARASON PROBLEM 211
V.5. CENTRAL NEHARI SOLUTIONS 218
V.6. CENTRAL NUDELMAN SOLUTIONS 227
V.7. THE CENTRAL TWO BLOCK SOLUTION 239
V.8. THE FOUR BLOCK PROBLEM 250
NOTES TO CHAPTER V 259
VI. PARAMETERIZATION OF INTERTWINING LIFTINGS AND ITS
APPLICATIONS 261
VI.l. THE MOBIUS TRANSFORMATION 261
VI.2. THE SCHUR PARAMETERIZATION 265
VI.3. RECOVERING THE SCHUR CONTRACTION 269
VIA CONSTRUCTING THE SCHUR CONTRACTION 271
VI.5. THE REDHEFFER SCATTERING PARAMETERIZATION 278
VI.6. THE PARAMETERIZATION FOR ||A|| y 288
VI.7. THE NEVALINNA PICK PARAMETERIZATION 292
VI.8. THE NEHARI PARAMETERIZATION 297
VI.9. THE TWO BLOCK PARAMETERIZATION 302
NOTES TO CHAPTER VI 308
VII. APPLICATIONS TO CONTROL SYSTEMS 309
VII. 1. FEEDBACK CONTROL 309
VII.2. THE YOULA PARAMETERIZATION 313
VII.3. MIXED H~ AND H2 CONTROL PROBLEMS 318
VII.4. A TWO BLOCK CONTROL PROBLEM 327
VII.5. THE MULTIVARIABLE CASE 334
NOTES TO CHAPTER VII 341
x TABLE OF CONTENTS
PART B NONSTATIONARY INTERPOLATION AND TIME VARYING
SYSTEMS 343
VIII. NONSTATIONARY INTERPOLATION THEOREMS 345
VIII. 1. NONSTATIONARY NEVANLINNA PICK INTERPOLATION 345
VIII.2. NONSTATIONARY TANGENTIAL NEVANLINNA PICK
INTERPOLATION 347
VIII.3. NONSTATIONARY TANGENTIAL HERMITE FEJER
INTERPOLATION 350
VIII.4. NONSTATIONARY NEHARI INTERPOLATION 355
VIII.5. NONSTATIONARY SARASON INTERPOLATION 356
VIII.6. NONSTATIONARY NUDELMAN INTERPOLATION 357
VIII.7. NONSTATIONARY TWO SIDED SARASON INTERPOLATION 359
NOTES TO CHAPTER VIII 360
IX. NONSTATIONARY SYSTEMS AND POINT EVALUATION 363
IX. 1. TIME VARYING SYSTEMS 363
IX.2. NONSTATIONARY CONTROLLABILITY AND OBSERVABILITY 367
IX.3. POINT EVALUATION 373
IX.4. FROM NONSTATIONARY SYSTEMS TO STATIONARY SYSTEMS 378
IX.5. A NONSTATIONARY FILTERING PROBLEM 380
NOTES TO CHAPTER IX 382
X. REDUCTION TECHNIQUES: FROM NONSTATIONARY TO STATIONARY
AND VICE VERSA 383
X.I. SPATIAL FEATURES 383
X.2. OPERATOR FEATURES 387
NOTES TO CHAPTER X 392
TABLE OF CONTENTS xi
XL PROOFS OF THE NONSTATIONARY INTERPOLATION THEOREMS BY
REDUCTION TO THE STATIONARY CASE 393
XI. 1. THE STANDARD NONSTATIONARY NEVANLINNA PICK
INTERPOLATION THEOREM 393
XI.2. THE NONSTATIONARY VERSION OF NEHARFS THEOREM 401
XI.3. THE NONSTATIONARY SARASON INTERPOLATION THEOREM 410
XI.4. THE NONSTATIONARY VERSION OF NUDELMAN S THEOREM 414
XI.5. THE NONSTATIONARY TWO SIDED SARASON INTERPOLATION
THEOREM 419
NOTES TO CHAPTER XI 422
XII. A GENERAL COMPLETION THEOREM 423
XII. 1. THE THREE CHAINS COMPLETION THEOREM 423
XII.2. PROOF BY ONE STEP EXTENSIONS 430
XII.3. AN EXPLICIT SOLUTION OF THE THREE CHAINS COMPLETION
PROBLEM 433
XII.4. MAXIMUM ENTROPY 440
XII.5. A QUOTIENT FORMULA FOR THE CENTRAL INTERPOLANT 452
XII.6. THE CASWELL SCHUBERT THEOREM 461
NOTES TO CHAPTER XII 467
XIII. APPLICATIONS OF THE THREE CHAINS COMPLETION THEOREM
TO INTERPOLATION 469
XIII. 1. ABSTRACT NONSTATIONARY INTERPOLATION 469
XIII.2. APPLICATION TO NEVANLINNA PICK INTERPOLATION 473
XIII.3. APPLICATION TO THE NEHARI PROBLEM 475
XIII.4. APPLICATION TO THE TWO SIDED SARASON PROBLEM 476
XIII.5. APPLICATION TO THE NUDELMAN PROBLEM 478
XIII.6. THE THREE CHAINS COMPLETION PROBLEM AND THE FOUR
BLOCK PROBLEM 488
NOTES TO CHAPTER XIII 495
xii TABLE OF CONTENTS
XIV. PARAMETERIZATION OF ALL SOLUTIONS OF THE THREE CHAINS
COMPLETION PROBLEM 497
XIV.l. MAIN THEOREM 497
XIV.2. PROOF OF MAIN THEOREM (first part) 505
XIV.3. PROOF OF MAIN THEOREM (second part) 507
XIV.4. THE CASE OF DECREASING SPACES 518
XIV.5. THE NONSTATIONARY NEHARI PARAMETERIZATION 522
NOTES TO CHAPTER XIV 532
APPENDIX ON FACTORIZATION OF MATRIX VALUED FUNCTIONS 533
A.I. SQUARE OUTER SPECTRAL FACTORIZATIONS 533
A.2. INNER OUTER FACTORIZATIONS 545
NOTES TO APPENDIX 559
REFERENCES 561
LIST OF SYMBOLS 575
INDEX 581
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| id | DE-604.BV011711713 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:14:27Z |
| institution | BVB |
| isbn | 3764358890 0817658890 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007898075 |
| oclc_num | 38249800 |
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| owner_facet | DE-91G DE-BY-TUM DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-824 DE-11 DE-188 |
| physical | XII, 587 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Metric constrained interpolation, commutant lifting and systems C. Foias ... Basel ; Boston ; Berlin Birkhäuser 1998 XII, 587 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 100 Literaturverz. S. 561 - 573 Commutant Espace état, Méthodes de l' ram Fonction à valeur matricielle Interpolation ram Lineaire operatoren gtt Relèvement (Mathématiques) ram Interpolation Lifting theory State-space methods Zeitvariantes System (DE-588)4190654-8 gnd rswk-swf Liftungssatz (DE-588)4265072-0 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Zeitinvariantes System (DE-588)4213493-6 gnd rswk-swf H-unendlich-Kontrolltheorie (DE-588)4488490-4 gnd rswk-swf Kommutant (DE-588)4265073-2 gnd rswk-swf Zeitinvariantes System (DE-588)4213493-6 s Zeitvariantes System (DE-588)4190654-8 s Interpolation (DE-588)4162121-9 s Kommutant (DE-588)4265073-2 s Liftungssatz (DE-588)4265072-0 s H-unendlich-Kontrolltheorie (DE-588)4488490-4 s DE-604 Foiaş, Ciprian 1933-2020 Sonstige (DE-588)172077648 oth Operator theory 100 (DE-604)BV000000970 100 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007898075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Metric constrained interpolation, commutant lifting and systems Operator theory Commutant Espace état, Méthodes de l' ram Fonction à valeur matricielle Interpolation ram Lineaire operatoren gtt Relèvement (Mathématiques) ram Interpolation Lifting theory State-space methods Zeitvariantes System (DE-588)4190654-8 gnd Liftungssatz (DE-588)4265072-0 gnd Interpolation (DE-588)4162121-9 gnd Zeitinvariantes System (DE-588)4213493-6 gnd H-unendlich-Kontrolltheorie (DE-588)4488490-4 gnd Kommutant (DE-588)4265073-2 gnd |
| subject_GND | (DE-588)4190654-8 (DE-588)4265072-0 (DE-588)4162121-9 (DE-588)4213493-6 (DE-588)4488490-4 (DE-588)4265073-2 |
| title | Metric constrained interpolation, commutant lifting and systems |
| title_auth | Metric constrained interpolation, commutant lifting and systems |
| title_exact_search | Metric constrained interpolation, commutant lifting and systems |
| title_full | Metric constrained interpolation, commutant lifting and systems C. Foias ... |
| title_fullStr | Metric constrained interpolation, commutant lifting and systems C. Foias ... |
| title_full_unstemmed | Metric constrained interpolation, commutant lifting and systems C. Foias ... |
| title_short | Metric constrained interpolation, commutant lifting and systems |
| title_sort | metric constrained interpolation commutant lifting and systems |
| topic | Commutant Espace état, Méthodes de l' ram Fonction à valeur matricielle Interpolation ram Lineaire operatoren gtt Relèvement (Mathématiques) ram Interpolation Lifting theory State-space methods Zeitvariantes System (DE-588)4190654-8 gnd Liftungssatz (DE-588)4265072-0 gnd Interpolation (DE-588)4162121-9 gnd Zeitinvariantes System (DE-588)4213493-6 gnd H-unendlich-Kontrolltheorie (DE-588)4488490-4 gnd Kommutant (DE-588)4265073-2 gnd |
| topic_facet | Commutant Espace état, Méthodes de l' Fonction à valeur matricielle Interpolation Lineaire operatoren Relèvement (Mathématiques) Lifting theory State-space methods Zeitvariantes System Liftungssatz Zeitinvariantes System H-unendlich-Kontrolltheorie Kommutant |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007898075&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT foiasciprian metricconstrainedinterpolationcommutantliftingandsystems |