Hankel operators and their applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2003
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes |
| Beschreibung: | XV, 784 S. graph. Darst. |
| ISBN: | 0387955488 |
Internformat
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| 100 | 1 | |a Peller, Vladimir V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Hankel operators and their applications |c Vladimir Peller |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2003 | |
| 300 | |a XV, 784 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 4 | |a Hankel, Opérateurs de | |
| 650 | 7 | |a Operatortheorie |2 gtt | |
| 650 | 4 | |a Hankel operators | |
| 650 | 0 | 7 | |a Hankel-Operator |0 (DE-588)4314042-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Hankel-Operator |0 (DE-588)4314042-7 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804129326636990464 |
|---|---|
| adam_text | Contents
Chapter 1. An Introduction to Hankel Operators 1
1. Bounded Hankel Operators 2
2. Hankel Operators and Compressed Shift 13
3. Hankel Operators of Finite Rank 19
4. Interpolation Problems 23
5. Compactness of Hankel Operators 25
6. Hankel Operators and Reproducing Kernels 37
7. Hankel Operators and Moment Sequences 39
8. Hankel Operators as Integral Operators on the Semi Axis ... 46
Concluding Remarks 56
Chapter 2. Vectorial Hankel Operators 61
1. Completing Matrix Contractions 62
2. Bounded Block Hankel Matrices 66
3. Hankel Operators and the Commutant Lifting Theorem 71
4. Compact Vectorial Hankel Operators 74
5. Vectorial Hankel Operators of Finite Rank 76
6. Imbedding Theorems 81
Concluding Remarks 84
Chapter 3. Toeplitz Operators 87
1. Basic Properties 88
2. A General Invertibility Criterion 94
3. Spectra of Certain Toeplitz Operators 97
4. Toeplitz Operators on Spaces of Vector Functions 103
xii Contents
5. Wiener Hopf Factorizations of Symbols of Fredholm Toeplitz
Operators 109
6. Left Invertibility of Bounded Analytic Matrix Functions 119
Concluding Remarks 121
Chapter 4. Singular Values of Hankel Operators 125
1. The Adamyan Arov Krein Theorem 126
2. The Case sm(T) = s^T) 131
3. Finite Rank Approximation of Vectorial Hankel Operators .. 135
4. Relations between Hu and i/c 142
Concluding Remarks 145
Chapter 5. Parametrization of Solutions of the Nehari Problem .. 147
1. Adamyan Arov Krein Parametrization in the Scalar Case .. 148
2. Parametrization of Solutions of the Nevanlinna Pick
Problem 170
3. Parametrization of Solutions of the Nehari Takagi Problem . 173
4. Parametrization via One Step Extension 187
5. Parametrization in the General Case 212
Concluding Remarks 228
Chapter 6. Hankel Operators and Schatten von Neumann Classes 231
1. Nuclearity of Hankel Operators 232
2. Hankel Operators of Class Sp, 1 p oo 239
3. Hankel Operators of Class Sp, 0 p 1 243
4. Hankel Operators and Schatten Lorentz Classes 253
5. Projecting onto the Hankel Matrices 257
6. Rational Approximation 267
7. Other Applications of the Sp Criterion 275
8. Generalized Hankel Matrices 281
9. Generalized Block Hankel Matrices and Vectorial Hankel
Operators 292
Concluding Remarks 296
Chapter 7. Best Approximation by Analytic and Meromorphic
Functions 303
1. Function Spaces That Can Be Described in Terms of Rational
Approximation in BMO 306
2. Best Approximation in Decent Banach Algebras 312
3. Best Approximation in Spaces without a Norm 316
4. Examples and Counterexamples 318
5. Badly Approximable Functions 338
6. Perturbations of Multiple Singular Values of Hankel
Operators 341
7. The Boundedness Problem 344
Contents xiii
8. Arguments of Unimodular Functions 355
9. Schmidt Functions of Hankel Operators 356
10. Continuity in the sup Norm 359
11. Continuity in Decent Banach Spaces 362
12. The Recovery Problem in Spaces of Measures and Interpolation
by Analytic Functions 371
13. The Fefferman Stein Decomposition in BXJV 376
Concluding Remarks 376
Chapter 8. An Introduction to Gaussian Spaces 379
1. Gaussian Spaces 380
2. The Fock Space 384
3. Mixing Properties and Regularity Conditions 390
4. Minimality and Basisness 402
5. Scattering Systems and Hankel Operators 405
6. Geometry of Past and Future 408
Concluding Remarks 412
Chapter 9. Regularity Conditions for Stationary Processes 415
1. Minimality in Spectral Terms 415
2. Angles between Past and Future 417
3. Regularity Conditions in Spectral Terms 420
4. Stronger Regularity Conditions 424
Concluding Remarks 426
Chapter 10. Spectral Properties of Hankel Operators 431
1. The Essential Spectrum of Hankel Operators with Piecewise
Continuous Symbols 433
2. The Carleman Operator 440
3. Quasinilpotent Hankel Operators 443
Concluding Remarks 450
Chapter 11. Hankel Operators in Control Theory 453
1. Transfer Functions 454
2. Realizations with Discrete Time 457
3. Realizations with Continuous Time 466
4. Model Reduction 472
5. Robust Stabilization 473
6. Coprime Factorization 476
7. Proof of Theorem 5.1 479
8. Parametrization of Stabilizing Controllers 482
9. Solution of the Robust Stabilization Problem. The Model
Matching Problem 485
Concluding Remarks 487
xiv Contents
Chapter 12. The Inverse Spectral Problem for Self Adjoint Hankel
Operators 489
1. Necessary Conditions 493
2. Eigenvalues of Hankel Operators 497
3. Linear Systems with Continuous Time and Lyapunov
Equations 499
4. Construction of a Linear System with Continuous Time .... 503
5. The Kernel of J 509
6. Proofs of Lemmas 4.1 and 5.2 516
7. Positive Hankel Operators with Multiple Spectrum 518
8. Moduli of Hankel Operators, Past and Future, and the Inverse
Problem for Rational Approximation 520
9. Linear Systems with Discrete Time 522
10. Passing to Balanced Linear Systems 526
11. Asymptotic Stability 529
12. The Main Construction 531
13. Proof of Theorem 9.1 536
14. Proofs of Lemmas 13.2 and 13.5 542
15. A Theorem in Perturbation Theory 548
Concluding Remarks 550
Chapter 13. Wiener Hopf Factorizations and the Recovery
Problem 553
1. The Recovery Problem in 7^ spaces 554
2. Maximizing Vectors of Vectorial Hankel Operators 555
3. Wiener Masani Factorizations 557
4. Isometric Outer Factorizations 560
5. The Recovery Problem and Wiener Hopf Factorizations of
Unitary Valued Functions 561
6. Wiener Hopf Factorizations. The General Case 562
Concluding Remarks 563
Chapter 14. Analytic Approximation of Matrix Functions 565
1. Balanced Matrix Functions 568
2. Parametrization of Best Approximations 574
3. Superoptimal Approximation of H°° + C Matrix Functions . 578
4. Superoptimal Approximation of Matrix Functions $ with
Small Essential Norm of if $ 580
5. Thematic Factorizations and Very Badly Approximable
Functions 586
6. Admissible and Superoptimal Weights 592
7. Thematic Indices 594
8. Inequalities Involving Hankel and Superoptimal Singular
Values 600
9. Invariance of Residual Entries 602
Contents xv
10. Monotone Thematic Factorizations and Invariance of Thematic
Indices 607
11. Construction of Superoptimal Approximation and the Corona
Problem 615
12. Hereditary Properties of Superoptimal Approximation 618
13. Continuity Properties of Superoptimal Approximation 623
14. Unitary Interpolants of Matrix Functions 636
15. Canonical Factorizations 643
16. Very Badly Approximable Unitary Valued Functions 661
17. Superoptimal Meromorphic Approximation 662
18. Analytic Approximation of Infinite Matrix Functions 672
19. Back to the Adamyan Arov Krein Parametrization 681
Concluding Remarks 682
Chapter 15. Hankel Operators and Similarity to a Contraction .. 685
1. Operators R^ in the Scalar Case 687
2. Power Bounded Operators R^p 693
3. Counterexamples 694
Concluding Remarks 703
Appendix 1 705
Appendix 2 717
References 739
Author Index 776
Subject Index 780
|
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| indexdate | 2024-07-09T19:03:22Z |
| institution | BVB |
| isbn | 0387955488 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009891946 |
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| physical | XV, 784 S. graph. Darst. |
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| spelling | Peller, Vladimir V. Verfasser aut Hankel operators and their applications Vladimir Peller New York [u.a.] Springer 2003 XV, 784 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Includes bibliographical references and indexes Hankel, Opérateurs de Operatortheorie gtt Hankel operators Hankel-Operator (DE-588)4314042-7 gnd rswk-swf Hankel-Operator (DE-588)4314042-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009891946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peller, Vladimir V. Hankel operators and their applications Hankel, Opérateurs de Operatortheorie gtt Hankel operators Hankel-Operator (DE-588)4314042-7 gnd |
| subject_GND | (DE-588)4314042-7 |
| title | Hankel operators and their applications |
| title_auth | Hankel operators and their applications |
| title_exact_search | Hankel operators and their applications |
| title_full | Hankel operators and their applications Vladimir Peller |
| title_fullStr | Hankel operators and their applications Vladimir Peller |
| title_full_unstemmed | Hankel operators and their applications Vladimir Peller |
| title_short | Hankel operators and their applications |
| title_sort | hankel operators and their applications |
| topic | Hankel, Opérateurs de Operatortheorie gtt Hankel operators Hankel-Operator (DE-588)4314042-7 gnd |
| topic_facet | Hankel, Opérateurs de Operatortheorie Hankel operators Hankel-Operator |
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