Operators, functions, and systems: an easy reading Volume II Model operators and systems
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Weitere beteiligte Personen: | |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 93 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009815931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xiv, 438 Seiten |
| ISBN: | 0821828762 9780821852651 |
Internformat
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| 245 | 1 | 0 | |a Operators, functions, and systems |b an easy reading |n Volume II |p Model operators and systems |c Nikolai K. Nikolski. Translated by Andreas Hartmann |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 93 | |
| 490 | 0 | |a Mathematical surveys and monographs | |
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Datensatz im Suchindex
| _version_ | 1819357497662636032 |
|---|---|
| adam_text | Contents
A Few Words about the Book v
Part C. Model Operators and Free Interpolation 1
Foreword to Part C 5
Chapter 1. The Basic Function Model 9
1.1. Unitary Dilations 9
1.2. Functional Embeddings and the Characteristic Function 17
1.3. The Function Model and Its Transcriptions 28
1.4. Models for Certain Accretive and Dissipative Operators 35
1.5. Exercises and Further Results 43
1.6. Notes and Remarks 73
Chapter 2. Elements of Spectral Theory in the Language of the Characteristic
Function 87
2.1. Invariant Subspaces 87
2.2. The H°° Functional Calculus 97
2.3. The Class Co, Minimal Annihilators, and the Spectrum of Mq 100
2.4. The Commutant Lifting Theorem 104
2.5. Exercises and Further Results 106
2.6. Notes and Remarks 137
Chapter 3. Decompositions into Invariant Subspaces and Free Interpolation 153
3.1. Unconditional Bases 155
3.2. Generalized Free Interpolation 160
3.3. Exercises and Further Results 170
3.4. Notes and Remarks 191
Part D. Analytic Problems in Linear System Theory 197
Foreword to Part D 201
Chapter 1. Basic Theory 205
1.1. The Main Formula 205
1.2. Initial Observations about Controllability 205
1.3. Basic Criteria for ACO, ECO, and NCO 207
1.4. Stable Systems 218
1.5. An Example: Heating of a Metal Bar 220
1.6. Exercises and Further Results 222
1.7. Notes and Remarks 233
ix
x CONTENTS
Chapter 2. First Optimizations: Multiplicity of the Spectrum and the DISC 237
2.1. The Least Dimension of Controlling Subspaces 237
2.2. Reduction to Bounded Operators 238
2.3. Multiplicity of the Spectrum 241
2.4. The Minimal Dimension of Constrained (Realizable) Control 247
2.5. Exercises and Further Results 254
2.6. Notes and Remarks 262
Chapter 3. Eigenvector Decompositions, Vector Valued Exponentials, and
Squared Optimization 267
3.1. Examples of Parabolic and Hyperbolic Systems 268
3.2. Complete Generators 271
3.3. Riesz Bases and Exact Controllability 274
3.4. Generalized Controllability and Renormalizations 277
3.5. NuU Controllability (NCO) 284
3.6. Weak Controllability 289
3.7. Squared (Energy) Optimization 290
3.8. Control at Time t = oo and Interpolation in H2 293
3.9. Notes and Remarks 295
Chapter 4. A Glance at Bases of Exponentials and of Reproducing Kernels 299
4.1. Small Perturbations of Harmonic Frequencies 300
4.2. Bases of Exponentials on the Half-Line 301
4.3. Bases of Exponentials on Finite Intervals 304
4.4. Bases of Reproducing Kernels in Model Spaces 307
4.5. Back to Exponentials 313
4.6. A Levinson Completeness Theorem 316
4.7. Exercises and Further Results 321
4.8. Notes and Remarks 334
Chapter 5. A Brief Introduction to H°° Control 343
5.1. Input-Output Maps and Transfer Functions 343
5.2. Noise Minimization, Feedback Control, and Sensitivity 346
5.3. Remarks on Robust Stabilization 350
5.4. Scattering Type Input-Output, and Hankel Operators 350
5.5. Remarks on Finite Dimensional Systems 355
5.6. Exercises and Further Results 356
5.7. Notes and Remarks 358
Bibliography 361
Author Index 401
Subject Index 411
Symbol Index 435
Errata to Volume 1 439
|
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| id | DE-604.BV014308806 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:03:00Z |
| institution | BVB |
| isbn | 0821828762 9780821852651 |
| language | English |
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| physical | xiv, 438 Seiten |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Nikolski, Nikolai K. 1940- Operators, functions, and systems an easy reading Mathematical surveys and monographs |
| title | Operators, functions, and systems an easy reading |
| title_auth | Operators, functions, and systems an easy reading |
| title_exact_search | Operators, functions, and systems an easy reading |
| title_full | Operators, functions, and systems an easy reading Volume II Model operators and systems Nikolai K. Nikolski. Translated by Andreas Hartmann |
| title_fullStr | Operators, functions, and systems an easy reading Volume II Model operators and systems Nikolai K. Nikolski. Translated by Andreas Hartmann |
| title_full_unstemmed | Operators, functions, and systems an easy reading Volume II Model operators and systems Nikolai K. Nikolski. Translated by Andreas Hartmann |
| title_short | Operators, functions, and systems |
| title_sort | operators functions and systems an easy reading model operators and systems |
| title_sub | an easy reading |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009815931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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