Carleson curves, Muckenhoupt weights, and Toeplitz operators:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1997
|
| Series: | Progress in mathematics
154 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007897582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XV, 397 S. Ill., graph. Darst. |
| ISBN: | 3764357967 0817657967 |
Staff View
MARC
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| 100 | 1 | |a Böttcher, Albrecht |d 1954- |e Verfasser |0 (DE-588)110234979 |4 aut | |
| 245 | 1 | 0 | |a Carleson curves, Muckenhoupt weights, and Toeplitz operators |c Albrecht Böttcher ; Yuri I. Karlovich |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a XV, 397 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 154 | |
| 650 | 7 | |a Opérateurs intégraux |2 ram | |
| 650 | 7 | |a Toeplitz, Opérateurs de |2 ram | |
| 650 | 4 | |a Integral operators | |
| 650 | 4 | |a Toeplitz operators | |
| 650 | 0 | 7 | |a Toeplitz-Operator |0 (DE-588)4191521-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007897582 | |
Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 358f 2001 A 8400 |
|---|---|
| DE-BY-TUM_katkey | 883640 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020208135 |
| _version_ | 1821931535523119104 |
| adam_text | Contents
Preface xiii
1 Carleson curves
1.1 Definitions and examples 1
1.2 Growth of the argument 8
1.3 Seifullayev bounds 11
1.4 Submultiplicative functions 13
1.5 The W transform 15
1.6 Spirality indices 18
1.7 Notes and comments 26
2 Muckenhoupt weights
2.1 Definitions 27
2.2 Power weights 30
2.3 The logarithm of a Muckenhoupt weight 32
2.4 Symmetric and periodic reproduction 35
2.5 Portions versus arcs 39
2.6 The maximal operator 44
2.7 The reverse Holder inequality 48
2.8 Stability of Muckenhoupt weights 56
2.9 Muckenhoupt condition and W transform 59
2.10 Oscillating weights 66
2.11 Notes and comments 68
3 Interaction between curve and weight
3.1 Moduli of complex powers 71
3.2 U and V transforms 73
3.3 Muckenhoupt condition and U transform 79
ix
x Contents
3.4 Indicator set and U transform 84
3.5 Indicator functions 90
3.6 Indices of powerlikeness 97
3.7 Shape of the indicator functions 101
3.8 Indicator functions of prescribed shape 105
3.9 Notes and comments 114
4 Boundedness of the Cauchy singular integral
4.1 The Cauchy singular integral 117
4.2 Necessary conditions for boundedness 123
4.3 Special curves and weights 130
4.4 Brief survey of results on general curves and weights 137
4.5 Composing curves and weights 139
4.6 Notes and comments 144
5 Weighted norm inequalities
5.1 Again the maximal operator 145
5.2 The Calderon Zygmund decomposition 149
5.3 Cotlar s inequality 151
5.4 Good A inequalities 157
5.5 Modified maximal operators 160
5.6 The maximal singular integral operator 165
5.7 Lipschitz curves 171
5.8 Measures in the plane 184
5.9 Cotlar s inequality in the plane 187
5.10 Maximal singular integrals in the plane 190
5.11 Approximation by Lipschitz curves 194
5.12 Completing the puzzle 198
5.13 Notes and comments 199
6 General properties of Toeplitz operators
6.1 Smirnov classes 204
6.2 Weighted Hardy spaces 207
6.3 Fredholm operators 211
6.4 Toeplitz operators 213
6.5 Adjoints 215
6.6 Two basic theorems 217
6.7 Hankel operators 219
6.8 Continuous symbols 221
Contents xi
6.9 Classical Toeplitz matrices 222
6.10 Separation of discontinuities 225
6.11 Localization 226
6.12 Wiener Hopf factorization 228
6.13 Notes and comments 231
7 Piecewise continuous symbols
7.1 Local representatives 235
7.2 Fredholm criterion 240
7.3 Leaves and essential spectrum 242
7.4 Metamorphosis of leaves 243
7.5 Logarithmic leaves 247
7.6 General leaves 252
7.7 Index and spectrum 258
7.8 Semi Fredholmness 261
7.9 Notes and comments 265
8 Banach algebras
8.1 General theorems 267
8.2 Operators of local type 270
8.3 Algebras generated by idempotents 273
8.4 An N projections theorem 275
8.5 Algebras associated with Jordan curves 288
8.6 Notes and comments 297
9 Composed curves
9.1 Extending Carleson stars 301
9.2 Extending Muckenhoupt weights 304
9.3 Operators on flowers 316
9.4 Local algebras 320
9 5 Symbol calculus 326
9 6 Essential spectrum of the Cauchy singular integral 329
9.7 Notes and comments 332
10 Further results
10.1 Matrix case 337
10.2 Index formulas 340
10.3 Kernel and cokernel dimensions 345
10.4 Spectrum of the Cauchy singular integral 346
xii Contents
10.5 Orlicz spaces 349
10.6 Mellin techniques 355
10.7 Wiener Hopf integral operators 367
10.8 Zero order pseudodifferential operators 372
10.9 Conformal welding and Baseman s problem 374
10.10 Notes and comments 379
Bibliography 381
Index 392
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| any_adam_object | 1 |
| author | Böttcher, Albrecht 1954- Karlovič, Jurij I. 1949- |
| author_GND | (DE-588)110234979 (DE-588)115613099 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7246 |
| dewey-search | 515/.7246 |
| dewey-sort | 3515 47246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011711125 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:17:19Z |
| institution | BVB |
| isbn | 3764357967 0817657967 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007897582 |
| oclc_num | 37588515 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-824 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-824 DE-11 DE-188 |
| physical | XV, 397 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Böttcher, Albrecht 1954- Karlovič, Jurij I. 1949- Carleson curves, Muckenhoupt weights, and Toeplitz operators Progress in mathematics Opérateurs intégraux ram Toeplitz, Opérateurs de ram Integral operators Toeplitz operators Toeplitz-Operator (DE-588)4191521-5 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4191521-5 (DE-588)4116561-5 |
| title | Carleson curves, Muckenhoupt weights, and Toeplitz operators |
| title_auth | Carleson curves, Muckenhoupt weights, and Toeplitz operators |
| title_exact_search | Carleson curves, Muckenhoupt weights, and Toeplitz operators |
| title_full | Carleson curves, Muckenhoupt weights, and Toeplitz operators Albrecht Böttcher ; Yuri I. Karlovich |
| title_fullStr | Carleson curves, Muckenhoupt weights, and Toeplitz operators Albrecht Böttcher ; Yuri I. Karlovich |
| title_full_unstemmed | Carleson curves, Muckenhoupt weights, and Toeplitz operators Albrecht Böttcher ; Yuri I. Karlovich |
| title_short | Carleson curves, Muckenhoupt weights, and Toeplitz operators |
| title_sort | carleson curves muckenhoupt weights and toeplitz operators |
| topic | Opérateurs intégraux ram Toeplitz, Opérateurs de ram Integral operators Toeplitz operators Toeplitz-Operator (DE-588)4191521-5 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Opérateurs intégraux Toeplitz, Opérateurs de Integral operators Toeplitz operators Toeplitz-Operator Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007897582&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT bottcheralbrecht carlesoncurvesmuckenhouptweightsandtoeplitzoperators AT karlovicjuriji carlesoncurvesmuckenhouptweightsandtoeplitzoperators |
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| Call Number: |
0102 MAT 358f 2001 A 8400
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