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Analysis of Toeplitz Operators
von: Albrecht Böttcher, Bernd Silbermann
Springer-Verlag, 2006
ISBN: 9783540324362 , 665 Seiten
2. Auflage
Format: PDF, OL
Kopierschutz: Wasserzeichen
Preis: 117,69 EUR
Preface to the Second Edition
5
Preface to the First Edition
7
Contents
11
1 Auxiliary Material
14
1.1 Operator Ideals
14
1.2 Operator Determinants
17
1.3 Fredholm Operators
22
1.4 Operator Matrices and Their Determinants
24
1.5 Banach Algebras
25
1.6 C*- Algebras
30
1.7 Local Principles
34
1.8 Lp and Hp
40
1.9 BMO and VMO
49
1.10 Smoothness Classes
51
1.11 Notes and Comments
54
2 Basic Theory
57
2.1 Multiplication Operators
57
2.2 Toeplitz Operators
61
2.3 Hankel Operators
64
2.4 Invertibility of Toeplitz Operators on H2
69
2.5 Spectral Inclusion Theorems
76
2.6 The Connection Between Fredholmness and Invertibility
83
2.7 Compactness of Hankel Operators and C + H8 Symbols
89
2.8 Local Methods for Scalar Toeplitz Operators
97
2.9 Matrix Symbols
111
2.10 Notes and Comments
115
3 Symbol Analysis
122
3.1 Local Sectoriality
122
3.2 Asymptotic Multiplicativity
130
3.3 Piecewise Quasicontinuous Functions
139
3.4 Harmonic Approximation: Algebraization
151
3.5 Harmonic Approximation: Essentialization
160
3.6 Harmonic Approximation: Localization
163
3.7 Harmonic Approximation: Local Spectra
168
3.8 Local Sectoriality Continued
177
3.9 Notes and Comments
180
4 Toeplitz Operators on H2
182
4.1 Fredholmness
182
4.2 Stable Convergence
189
4.3 Index Computation
198
4.4 Transfinite Localization
202
4.5 Local Toeplitz Operators
222
4.6 Symbols with Specific Local Range
228
4.7 Toeplitz Algebras
237
4.8 The Role of the Harmonic Extension
251
4.9 Notes and Comments
255
5 Toeplitz Operators on Hp
259
5.1 General Theorems
259
5.2 Khvedelidze Weights
263
5.3 Locally p, -Sectorial Symbols
264
5.4 Localization
274
5.5 PC Symbols
277
5.6 P2C Symbols
287
5.7 Fisher-Hartwig Symbols
291
5.8 Notes and Comments
293
6 Toeplitz Operators on
297
6.1 Multipliers on Weighted
297
Spaces
297
6.2 Continuous Symbols
303
6.3 Piecewise Continuous Symbols
307
6.4 Analytic Symbols
318
6.5 Notes and Comments
330
7 Finite Section Method
333
7.1 Basic Facts
333
7.2 C + H8 Symbols
345
7.3 Locally Sectorial Symbols
354
7.4 PC Symbols:
357
Theory
357
7.5 PC Symbols: Hp Theory
363
7.6 Operators from alg
367
T (PC)
367
7.7 Fisher-Hartwig Symbols: H2( ) Theory
384
7.8 Fisher-Hartwig Symbols:
388
Theory
388
7.9 Invertibility Versus Finite
399
Section
399
Method
399
7.10 Pseudospectra
404
7.11 Notes and Comments
410
8 Toeplitz Operators over the Quarter-Plane
418
8.1 Function Classes on the Torus
418
8.2 Elementary Properties of Quarter-Plane Operators
426
8.3 Continuous Symbols
430
8.4 The Invertibility Problem
437
8.5 Bilocal Fredholm Theory
447
8.6 PQC . PQC Symbols
457
8.7 Finite Section Method: Kozak’s Theory
463
8.8 Finite Section Method: Bilocal Theory
470
8.9 Higher Dimensions
479
8.10 Notes and Comments
484
9 Wiener-Hopf Integral Operators
489
9.1 Basic Properties
489
9.2 Continuous Symbols
494
9.3 Piecewise Continuous Symbols
496
9.4 AP and SAP Symbols
500
9.5 Some Phenomena Caused by SAP Symbols
505
9.6 Other Oscillating Symbols
509
9.7 Finite Section Method
512
9.8 Operators over the Quarter Plane
521
9.9 Notes and Comments
528
10 Toeplitz Determinants
533
10.1 The First Szeg. o Limit Theorem
533
10.2 Krein Algebras
537
10.3 Wiener-Hopf Factorization
541
10.4 The Strong Szeg. o Limit Theorem
545
10.5 Higher Order Asymptotics
551
10.6 Semirational Symbols
562
10.7 Nonvanishing Index
566
10.8 Selfadjoint Symbols
574
10.9 The Pure Fisher-Hartwig Singularity
578
10.10 Separation Theorems
580
10.11 Fisher-Hartwig Symbols
590
10.12 More on Unbounded Symbols
600
10.13 Wiener-Hopf Determinants
603
10.14 Eigenvalues
613
10.15 Notes and Comments
619
References
628
A
628
B
629
C
634
D
635
E
637
F
638
G
638
H
641
I
643
J
643
K
643
L
645
M
646
N
647
O
647
P
647
R
649
S
651
T
654
U
655
V
655
W
656
X
658
Y
658
Z
658
Notation
659
Index
666
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