One-dimensional linear singular integral equations: 2 General theory and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel u.a.
Birkhäuser
1992
|
| Schriftenreihe: | Operator theory
54 |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 232 S. graph. Darst. |
| ISBN: | 3764327960 0817627960 |
Internformat
MARC
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| 100 | 1 | |a Gohberg, Yiśrāʿēl Z. |d 1928-2009 |e Verfasser |0 (DE-588)118915878 |4 aut | |
| 240 | 1 | 0 | |a Vvedenie v teoriju odnomernych singuljarnych integralʹnych operatorov |
| 245 | 1 | 0 | |a One-dimensional linear singular integral equations |n 2 |p General theory and applications |c Israel Gohberg ; Naum Krupnik |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1992 | |
| 300 | |a 232 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 54 | |
| 490 | 0 | |a Operator theory |v ... | |
| 700 | 1 | |a Krupnik, Nahum |d 1932- |e Verfasser |0 (DE-588)121758400 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804120036316545024 |
|---|---|
| adam_text | Contents
Preface 9
Introduction 11
6 Preliminaries 15
6.1 The operator of singular integration 15
6.2 The space Lp{T,p) 16
6.3 Singular integral operators 17
6.4 The spaces L+(l», L;{T,p) and L; (T,p) 19
6.5 Factorization 20
6.6 One sided invertibility of singular integral operators 21
6.7 Fredholm operators 22
6.8 The local principle for singular integral operators 24
6.9 The interpolation theorem 25
7 General theorems 27
7.1 Change of the curve 27
7.2 The quotient norm of singular integral operators 30
7.3 The principle of separation of singularities 34
7.4 A necessary condition 37
7.5 Theorems on kernel and cokernel of singular integral operators 39
7.6 Two theorems on connections between singular integral operators 41
7.7 Index cancellation and approximative inversion of singular integral operators 43
7.8 Exercises 45
Comments and references 47
8 The generalized factorization of bounded measurable functions and its
applications 49
8.1 Sketch of the problem 49
5
6 CONTENTS
8.2 Functions admitting a generalized factorization with respect to a curve in
LP(T,P) 51
8.3 Factorization in the spaces LP(T, p) 53
8.4 Application of the factorization to the inversion of singular integral operators 56
8.5 Exercises 58
Comments and references 60
9 Singular integral operators with piecewise continuous coefficients and their
applications 61
9.1 Non singular functions and their index 62
9.2 Criteria for the generalized factorizability of power functions 65
9.3 The inversion of singular integral operators on a closed curve 70
9.4 Composed curves 73
9.5 Singular integral operators with continuous coefficients on a composed curve 81
9.6 The case of the real axis .* 93
9.7 Another method of inversion 95
9.8 Singular integral operators with regel functions coefficients 99
9.9 Estimates for the norms of the operators Pp, Qr and Sr 101
9.10 Singular operators on spaces H°(T,p) 103
9.11 Singular operators on symmetric spaces 105
9.12 Fredholm conditions in the case of arbitrary weights 108
9.13 Technical lemmas 111
9.14 Toeplitz and paired operators with piecewise continuous coefficients on the
spaces lp and lp 115
9.15 Some applications 122
9.16 Exercises 145
Comments and references 148
10 Singular integral operators on non simple curves 151
10.1 Technical lemmas 151
10.2 A preliminary theorem 156
10.3 The main theorem 159
10.4 Exercises 163
Comments and references 164
11 Singular integral operators with coefficients having discontinuities of al¬
most periodic type 165
11.1 Almost periodic functions and their factorization 165
11.2 Lemmas on functions with discontinuities of almost periodic type 167
CONTENTS 7
11.3 The main theorem 170
11.4 Operators with continuous coefficients the degenerate case 176
11.5 Exercises 178
Comments and references 178
12 Singular integral operators with bounded measurable coefficients 181
12.1 Singular operators with measurable coefficients in the space L^iT) 181
12.2 Necessary conditions in the space ^(T) 183
12.3 Lemmas 185
12.4 Singular operators with coefficients in pp(T) . Sufficient conditions 188
12.5 The Helson Szego theorem and its generalization 191
12.6 On the necessity of the condition a 6 Sp 194
12.7 Extension of the class of coefficients 196
12.8 Exercises 197
Comments and references 198
13 Exact constants in theorems on the boundedness of singular operators 199
13.1 Norm and quotient norm of the operator of singular integration 199
13.2 A second proof of Theorem 4.1 of Chapter 12 206
13.3 Norm and quotient norm of the operator Sp on weighted spaces 206
13.4 Conditions for Fredholmness in spaces Lp(P,p) 210
13.5 Norms and quotient norm of the operator al + bSr 213
13.6 Exercises 219
Comments and references 221
References 223
Subject Index 231
|
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| author | Gohberg, Yiśrāʿēl Z. 1928-2009 Krupnik, Nahum 1932- |
| author_GND | (DE-588)118915878 (DE-588)121758400 |
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| id | DE-604.BV005846462 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:35:42Z |
| institution | BVB |
| isbn | 3764327960 0817627960 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003660747 |
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| physical | 232 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Birkhäuser |
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| series | Operator theory |
| series2 | Operator theory |
| spelling | Gohberg, Yiśrāʿēl Z. 1928-2009 Verfasser (DE-588)118915878 aut Vvedenie v teoriju odnomernych singuljarnych integralʹnych operatorov One-dimensional linear singular integral equations 2 General theory and applications Israel Gohberg ; Naum Krupnik Basel u.a. Birkhäuser 1992 232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Operator theory 54 Operator theory ... Krupnik, Nahum 1932- Verfasser (DE-588)121758400 aut (DE-604)BV004756077 2 Operator theory 54 (DE-604)BV000000970 54 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003660747&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gohberg, Yiśrāʿēl Z. 1928-2009 Krupnik, Nahum 1932- One-dimensional linear singular integral equations Operator theory |
| title | One-dimensional linear singular integral equations |
| title_alt | Vvedenie v teoriju odnomernych singuljarnych integralʹnych operatorov |
| title_auth | One-dimensional linear singular integral equations |
| title_exact_search | One-dimensional linear singular integral equations |
| title_full | One-dimensional linear singular integral equations 2 General theory and applications Israel Gohberg ; Naum Krupnik |
| title_fullStr | One-dimensional linear singular integral equations 2 General theory and applications Israel Gohberg ; Naum Krupnik |
| title_full_unstemmed | One-dimensional linear singular integral equations 2 General theory and applications Israel Gohberg ; Naum Krupnik |
| title_short | One-dimensional linear singular integral equations |
| title_sort | one dimensional linear singular integral equations general theory and applications |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003660747&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004756077 (DE-604)BV000000970 |
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