Introduction to the theory of singular integral operators with shift:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1994
|
| Series: | Mathematics and its applications
289 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XVI, 288 S. |
| ISBN: | 0792328647 |
Staff View
MARC
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| 100 | 1 | |a Kravčenko, Viktor G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to the theory of singular integral operators with shift |c by Victor G. Kravchenko and Georgii S. Litvinchuk |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1994 | |
| 300 | |a XVI, 288 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 289 | |
| 500 | |a Aus dem Russ. übers. | ||
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Record in the Search Index
| _version_ | 1804124094297276416 |
|---|---|
| adam_text | CONTENTS
Introduction xi
Chapter 1. Background information 1
§1. On Noetherian operators 1
§2. On the operator of singular integration 15
§3. On the shift function and shift operator 26
§4. On C* algebras 33
Chapter 2. Noetherity criterion and a formula for the index of a singular integral
functional operator of first order in the continuous case 37
§1. Criterion of Noetherity for singular integral functional operators of first order
with orientation preserving shift 40
1.1. Criterion of Noetherity for the singular integral operator with a Cauchy
kernel 40
1.2. Abstract scheme for the study of the Noetherity of paired operators ... .41
1.3. A criterion of Noetherity for singular integral functional operators of the
first order in the case of a Carleman shift 44
1.4. A criterion of Noetherity for singular integral functional operators of first
order in the case of a non Carleman shift with a finite number of fixed
points 46
1.5. Noetherity criterion for a singular integral functional operator of first or¬
der in the case of a non Carleman shift having a finite number of periodic
points 55
1.6. Noetherity criterion for a singular integral functional operator of first order
with a shift having any non empty set of periodic points 56
§2. The calculation of the index of a singular integral functional operator of the first
order with a shift preserving the orientation 60
2.1. The index of a singular integral operator with a Cauchy kernel 60
VI TABLE OF CONTENTS
2.2. The index of a singular integral functional operator of the Kveselava Vekua
type 62
2.3. The calculation of the index of a singular integral functional operator of the
first order in the case of Carleman shift 66
2.4. The calculation of the index of a singular integral functional operator of the
first order with a shift having a finite number of fixed points 71
2.5. The calculation of the index of a singular integral functional operator of
the first order with a shift having a finite number of periodic points with
multiplicity k 72
2.6. The calculation of the index of a singular integral functional operator of
the first order with a shift having an arbitrary non empty set of periodic
points 73
§3. The Noetherity criterion and the index formula for a singular integral functional
operator of the first order with a shift changing the orientation 81
3.1. Reduced and associated operators. The connection between the Noetherity
of a singular integral functional operator with a shift changing the orienta¬
tion and the Noetherity of a reduced operator 81
3.2. Noetherity criterion and index formula for a singular integral functional op¬
erator of the first order with a Carleman shift changing the
orientation 84
3.3. Noetherity criterion and index formula for a singular integral functional op¬
erator of the first order with a non Carleman shift changing the
orientation 86
§ 4. References and a survey of similar or closed results 89
4.1. On weighted shift operators 89
4.2. On the one sided invertibility of functional operators and on the semi Noetherity
of singular integral functional operators of the first order in the space
LP(Y) 93
4.3. On functional and singular integral functional operators of the first order in
Holder and Orlicz spaces 94
4.4. On functional and singular integral functional operators of the first order with
a non invertible shift 96
TABLE OF CONTENTS vii
4.5. On singular integral functional operators of the first order with a shift which has
an empty set of periodic points 97
4.6. For the question of invertibility and one sided invertibility of singular integral
functional operators on a closed contour 98
Chapter 3. The Noether theory of a singular integral functional operator of finite order
in the continuous case 101
§ 1. The Noetherity criterion and the index formula for a system of singular in¬
tegral equations with a Cauchy kernel and continuous coefficients on a closed
contour 104
§ 2. Theorems concerning decreasing the order of functional and singular integral
operators 107
§ 3. Noetherity criterion and a formula for the index for systems of singular integral
equation with a Carleman shift 113
3.1. The case of an orientation preserving Carleman shift 113
3.2. The case of an orientation changing Carleman shift 117
§4. An invertibility criterion for a matrix functional operator with a non Carleman
shift 118
4.1. The reasons for the necessary conditions of invertibility 118
4.2. Invertibility conditions in the cases k( z) = 0 and k(o) = n 120
4.3. On the invertibility of a canonical functional operator with a matrix function
a reducible to the normal form 121
4.4. Q reducibility of a block triangular matrix to the normal form 123
4.5. A normalizable matrix of solutions of a functional equation system. A con¬
nection between a reducibility and normalizability 124
4.6. Lemma on the existence of a normalizable matrix of continuous solutions of
a functional equation 127
4.7. Local Q reducibility 133
4.8. On local properties of fundamental solutions 134
4.9. A fundamental system of solutions and its connection with the invertibility
of the canonical operator 137
4.10. A connection between the normalizability and existence of a fundamental
system of solution 140
viii TABLE OF CONTENTS
4.11. A criterion of invertibility for a canonical functional operator 141
4.12. A criterion for the invertibility of a functional operator of theorder m. The
case of a finite set of fixed points of shift 142
4.13. A matrix functional operator of the order m belongs to the set
M{S) 145
4.14. An invertibility criterion for a functional operator of the order m. The case
of a finite set of periodic points of the shift 146
§ 5. Noether theory for singular integral functional operators of superior
orders 148
5.1. The case of a shift that preserves the orientation on T and has a finite
number of fixed points 148
5.2. The case of a shift preserving the orientation on T with periodic
points 151
5.3. The case of a shift changing the orientation on F 152
§ 6. References and a survey of similar results 154
6.1. The invertibility of the matrix functional operator and its connection with
the spectral theory of dynamics systems and the multiplicative ergodic the¬
orem 154
Chapter 4. The Noether theory of singular integral functional operators with contin¬
uous coefficients on a non closed contour 161
§ 1. The Noetherity criterion and the index formula for a singular integral operator
with continuous coefficients on a non closed contour 164
1.1. An abstract scheme for the study of the Noetherity of paired operators on
a non closed contour 164
1.2. The reduction of the (/ — 52) Noetherity of a singular integral operator
with Cauchy kernel and continuous coefficients on the segment [0,1] to
the continuous invertibility of a singular integral operator with constant
coefficients 168
1.3. The spectral representation of the operator S. An invertibility criterion for
singular integral operators with constant coefficients 169
1.4. The Noetherity criterion and the index formula for a singular integral oper¬
ator with Cauchy kernel 172
TABLE OF CONTENTS ix
1.5. Operators with fixed singularities 177
1.6. The Noetherity criterion and the index formula for operators of the
algebra £ 180
1.7. Systems of singular integral equations on a non closed contour 184
§ 2. The Noetherity criterion and the index formula for singular integral functional
operators with continuous coefficients on a non closed contour 186
2.1. On the application of the abstract scheme for the study of
Noetherity 186
2.2. Some more results about operators with fixed singularities 188
2.3. The Noetherity criterion for the operator N 192
2.4. The index formula for the operator N 194
2.5. The Kveselava Vekua operator on a non closed contour 198
§ 3. Systems of singular integral operators with shift on a non closed contour .. 202
3.1. The criterion for Noetherity 202
3.2. The calculation of the index 204
3.3. The case of orientation changing shift 207
§ 4. References and a survey of closely related results 208
4.1. On the question of invertibility and one sided invertibility for singular inte¬
gral functional operators on a non closed contour 209
Chapter 5. The Noether theory in algebras of singular integral functional
operators 211
§ 1. C* algebras of singular integral operators 214
1.1. General scheme 214
1.2. Algebras of an SIO on a closed contour 217
1.3. Algebras of an SIO on a non closed contour 218
§ 2. C* algebras of singular integral operators with a Carleman shift 221
2.1. The case of a closed contour and an orientation preserving shift 221
2.2. The case of a closed contour and an orientation changing shift 222
2.3. The case of a non closed contour and an orientation changing Carleman
shift 223
X TABLE OF CONTENTS
§ 3. C* algebras of singular integral operators with non Carleman shift which has periodic
points 228
3.1. The case of a closed contour 228
3.2. The case of a non closed contour 232
3.3. Discrete operators 235
§ 4. Further development of a local method for studying the Noetherity of bounded linear
operators of non local type and its applications. Commentaries to the
literature 238
4.1. The local method (see Ju. I. Karlovich V. G. Kravchenko 8)) 239
4.2. On the local methods of Ju. I. Karlovich and their applications 248
4.3. On the factoribility of almost periodic matrix functions and the Noetherity of
certain classes of convolution type operators 257
References 265
Subject Index 287
|
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| indexdate | 2024-07-09T17:40:12Z |
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| isbn | 0792328647 |
| language | English |
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| physical | XVI, 288 S. |
| publishDate | 1994 |
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| publisher | Kluwer Acad. Publ. |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Kravčenko, Viktor G. Verfasser aut Introduction to the theory of singular integral operators with shift by Victor G. Kravchenko and Georgii S. Litvinchuk Dordrecht u.a. Kluwer Acad. Publ. 1994 XVI, 288 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 289 Aus dem Russ. übers. Verschiebungsoperator - Singulärer Integraloperator Verschiebungsoperator (DE-588)4121862-0 gnd rswk-swf Singulärer Integraloperator (DE-588)4131249-1 gnd rswk-swf Singulärer Integraloperator (DE-588)4131249-1 s DE-604 Verschiebungsoperator (DE-588)4121862-0 s DE-188 Litvinčuk, Georgij S. Verfasser aut Mathematics and its applications 289 (DE-604)BV008163334 289 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006447769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kravčenko, Viktor G. Litvinčuk, Georgij S. Introduction to the theory of singular integral operators with shift Mathematics and its applications Verschiebungsoperator - Singulärer Integraloperator Verschiebungsoperator (DE-588)4121862-0 gnd Singulärer Integraloperator (DE-588)4131249-1 gnd |
| subject_GND | (DE-588)4121862-0 (DE-588)4131249-1 |
| title | Introduction to the theory of singular integral operators with shift |
| title_auth | Introduction to the theory of singular integral operators with shift |
| title_exact_search | Introduction to the theory of singular integral operators with shift |
| title_full | Introduction to the theory of singular integral operators with shift by Victor G. Kravchenko and Georgii S. Litvinchuk |
| title_fullStr | Introduction to the theory of singular integral operators with shift by Victor G. Kravchenko and Georgii S. Litvinchuk |
| title_full_unstemmed | Introduction to the theory of singular integral operators with shift by Victor G. Kravchenko and Georgii S. Litvinchuk |
| title_short | Introduction to the theory of singular integral operators with shift |
| title_sort | introduction to the theory of singular integral operators with shift |
| topic | Verschiebungsoperator - Singulärer Integraloperator Verschiebungsoperator (DE-588)4121862-0 gnd Singulärer Integraloperator (DE-588)4131249-1 gnd |
| topic_facet | Verschiebungsoperator - Singulärer Integraloperator Verschiebungsoperator Singulärer Integraloperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006447769&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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