Operators, functions, and systems: an easy reading Volume I Hardy, Hankel, and Toeplitz
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 92 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009780958&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | xiv, 461 Seiten |
| ISBN: | 0821810839 9780821849330 |
Internformat
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| 245 | 1 | 0 | |a Operators, functions, and systems |b an easy reading |n Volume I |p Hardy, Hankel, and Toeplitz |c Nikolai K. Nikolski. Translated by Andreas Hartmann |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
| 300 | |a xiv, 461 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 92 | |
| 490 | 0 | |a Mathematical surveys and monographs | |
| 700 | 1 | |a Hartmann, Andreas |4 trl | |
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| 830 | 0 | |a Mathematical surveys and monographs |v Volume 92 |w (DE-604)BV000018014 |9 92 | |
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Datensatz im Suchindex
| _version_ | 1819372713888710656 |
|---|---|
| adam_text | Contents
A Few Words about the Book v
Volume 1: Hardy, Hankel and Toeplitz
Part A. An Invitation to Hardy Classes 1
Chapter 1. Invariant. Subspaces of L2(fi) 7
1.1. Basic Definitions 7
1.2. Doubly Invariant Subspaces 8
1.3. Simply Invariant Subspaces, the Case //, = m 9
1.4. Inner Functions. A Uniqueness Theorem 10
1.5. Invariant Subspaces of L2 (/;,): the General Case 10
1.6. Exercises and Further Results 13
1.7. Notes and Remarks 17
Chapter 2. First Applications 21
2.1. Straightforward Corollaries 21
2.2. The Problem of Weighted Polynomial Approximation 22
2.3. A Probabilistic Interpretation 23
2.4. The Inner-Outer Factorization 2,3
2.5. Arithmetic of Inner Functions 24
2.6. A Characterization of Outer Functions 25
2.7. Szego Infimiim and the Ricsz Brothers Theorem 25
2.8. Exercises and Further Results 27
2.9. Notes and Remarks 28
Chapter 3. Hp Classes. Canonical Factorization 31
3.1. The Main Definition 31
3.2. Straightforward Properties 32
3.3. A Digression on Convolutions and Fourier series 32
3.4. Identifying iF(O) and H 34
3.5. Jensen s Formula and Jensen s Inequality 35
3.6. The Boundary Uniqueness Theorem 36
3.7. Blaschke Products 37
3.8. Nontangential Boundary Limits 39
3.9. The Riesz-Smirnov Canonical Factorization 41
3.10. Approximation by inner functions and Bla.schke products 44
3.11. Vector valued i?p-spaces and the Fatou theorem 46
3.12. Exercises and Further Results 54
3.13. Notes and Remarks 57
x CONTENTS
Chapter 4. Szego Infimum, and Generalized Phragmen-Lindelof Principle 65
4.1. Szego Infimum and Weighted Polynomial Approximation 65
4.2. How to Recognize an Outer Function 67
4.3. Locally Outer Functions 68
4.4. The Smirnov Class V 72
4.5. A Conformally Invariant Framework 72
4.6. The Generalized Phragmen-Lindelof Principle 73
4.7. Classical Examples 74
4.8. Exercises and Further Results 75
4.9. Notes and Remarks 87
Chapter 5. Harmonic Analysis in L2(T,/j) 93
5.1. Generalized Fourier Series 93
5.2. Bases of Exponentials in L2(T,fi) 96
5.3. Harmonic Conjugates 98
5.4. The Helson-Szego Theorem 99
5.5. An Example 102
5.6. Comments 103
5.7. Exercises and Further Results 104
5.8. Notes and Remarks 129
Chapter 6. Transfer to the Half-Plane 143
6.1. A Unitary Mapping from Z,p(T) to LP(R) 143
6.2. Cauchy Kernels and Fourier Transforms 144
6.3. The Hardy Spaces Hi = #P(C+) 144
6.4. Canonical Factorization and Other Properties 147
6.5. Invariant Subspaces 148
6.6. Exercises and Further Results 150
6.7. Notes and Remarks 151
Chapter 7. Time-Invariant Filtering 153
7.1. The Language of Signal Processing 153
7.2. Frequency Characteristics of Causal Filters 154
7.3. Design Problems (Filter Synthesis) 155
7.4. Inverse Analysis Problems, or How to Tackle a Filter 157
7.5. Exercises and Further Results 159
7.6. Notes and Remarks 160
Chapter 8. Distance Formulae and Zeros of the Riemann ^-Function 163
8.1. Distance Functions 163
8.2. Zeros and Singular Measures via Distance Functions 165
8.3. Localization of Zeros of the Riemann (^-Function 166
8.4. Invariant Subspaces Related to the ^-Function 169
8.5. Exercises and Further Results 170
8.6. Notes and Remarks 171
Part B. Hankel and Toeplitz Operators 173
Chapter 1. Hankel Operators and Their Symbols 179
1.1. Hankel Matrices and Hankel Operators 179
CONTENTS xi
1.2. The Hardy Space Representation 180
1.3. Symbols of Hankel Operators and the Nehari Theorem 181
1.4. Two Proofs of the Nehari Theorem 182
1.5. An appendix on Hilbert space operators 186
1.6. Exercises and Further Results 188
1.7. What is a Hankel operator? A brief survey 195
1.8. Notes and Remarks 205
Chapter 2. Compact Hankel Operators 211
2.1. Essential Norm and the Calkin Algebra 211
2.2. The Adamyan-Arov-Krein Version of Hartman s Theorem 212
2.3. The algebras H00 + C and QC, and Compact Commutators 214
2.4. Invariant Subspaces and Kronecker s Theorem 216
2.5. Exercises and Further Results 218
2.6. Notes and Remarks 224
Chapter 3. Applications to Nevanlinna-Pick Interpolation 227
3.1. Model Operators 227
3.2. Schur and Nevanlinna- Pick Interpolation 231
3.3. Structure of Interpolating Functions and Rational Approximations 233
3.4. Exercises and Further Results 236
3.5. Notes and Remarks 239
Chapter 4. Essential Spectrum. The First Step: Elements of Toeplitz
Operators 243
4.1. Definition and Existence of the Symbol 243
4.2. Spectral Inclusions 246
4.3. The Fundamental Inversion Theorem 249
4.4. A Local Theory of Semicommutators 252
4.5. Fredholm Theory of the Toeplitz Algebra algTH^+c 256
4.6. Wiener-Hopf and Hankel Operators on the Real Line 261
4.7. Exercises and Further Results 262
4.8. Notes and Remarks 269
Chapter 5. Essential Spectrum. The Second Step: The Hilbert Matrix and
Other Hankel Operators 281
5.1. Piecewise Continuous Functions 281
5.2. The Schur Test 282
5.3. The Hilbert Matrix 283
5.4. The Main Theorem on the Essential Spectrum 288
5.5. Essentially Quasi-Nilpotent. and Essentially Self-Adjoint Hankel
Operators, and Other Corollaries 292
5.6. Exercises and Further Results 293
5.7. Notes and Remarks 302
Chapter 6. Hankel and Toeplitz Operators Associated
with Moment Problems 309
6.1. The Power Moment Problem 309
6.2. Hankel Operators Associated with a Measure 311
6.3. An Integral representation 314
xii CONTENTS
6.4. The Trigonometric Moment Problem and Positive Toeplitz Forms 315
6.5. Exercises and Further Results 316
6.6. Notes and Remarks 324
Chapter 7. Singular Numbers of Hankel Operators 331
7.1. The Schmidt Decomposition 331
7.2. The Basic Adamyan-Arov-Krein Theorem 333
7.3. Multiplicative Properties of ,s-Functions 336
7.4. An Application to Interpolation by Meromorphic Functions:
The Schur-Takagi Problem 337
7.5. Exercises and Further Results 338
7.6. Notes and Remarks 346
Chapter 8. Trace Class Hankel Operators 351
8.1. The Main Theorem. Connection with Rational Approximation 351
8.2. Information about Besov Classes 352
8.3. Information about the Class i 354
8.4. An Integral Representation and the Proof of Peller s Theorem 355
8.5. Another Approach to Trace Class Hankel Operators 359
8.6. Hilbert-Schmidt and Other Schatten-von Neumann Classes p 360
8.7. Exercises and Further Results 361
8.8. Notes and Remarks 372
Chapter 9. Inverse Spectral Problems, Stochastic Processes and One-Sided
Invertibility 377
9.1. Inverse Spectral Problems for Hankel Operators 377
9.2. One-sided Invertibility of Toeplitz Operators and the
Operator Corona Problem 385
9.3. Exercises and Further Results 393
9.4. Notes and Remarks 396
Bibliography 401
Author Index 441
Subject Index 447
Symbol Index 459
|
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| id | DE-604.BV014261913 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:02:12Z |
| institution | BVB |
| isbn | 0821810839 9780821849330 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009780958 |
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| physical | xiv, 461 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 I Hardy, Hankel, and Toeplitz Nikolai K. Nikolski. Translated by Andreas Hartmann |
| title_fullStr | Operators, functions, and systems an easy reading Volume I Hardy, Hankel, and Toeplitz Nikolai K. Nikolski. Translated by Andreas Hartmann |
| title_full_unstemmed | Operators, functions, and systems an easy reading Volume I Hardy, Hankel, and Toeplitz Nikolai K. Nikolski. Translated by Andreas Hartmann |
| title_short | Operators, functions, and systems |
| title_sort | operators functions and systems an easy reading hardy hankel and toeplitz |
| title_sub | an easy reading |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009780958&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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