Differentiable operators and nonlinear equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Basel u.a.
Birkhäuser
1994
|
| Series: | Operator theory
66 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 280 S. graph. Darst. |
| ISBN: | 3764329297 0817629297 |
Staff View
MARC
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| 100 | 1 | |a Khatskevich, Victor |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differentiable operators and nonlinear equations |c Victor Khatskevich ; David Shoiykhet |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1994 | |
| 300 | |a X, 280 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 66 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Applications différentiables |2 ram | |
| 650 | 7 | |a Applications holomorphes |2 ram | |
| 650 | 7 | |a Banach, espaces de |2 ram | |
| 650 | 7 | |a Niet-lineaire vergelijkingen |2 gtt | |
| 650 | 7 | |a Operatortheorie |2 gtt | |
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Differentiable mappings | |
| 650 | 4 | |a Holomorphic mappings | |
| 650 | 0 | 7 | |a Holomorphe Abbildung |0 (DE-588)4160471-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Operator |0 (DE-588)4167721-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Analysis |0 (DE-588)4177490-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differenzierbarkeit |0 (DE-588)4149807-0 |2 gnd |9 rswk-swf |
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| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Shoiykhet, David |d 1953- |e Verfasser |0 (DE-588)1079700099 |4 aut | |
| 830 | 0 | |a Operator theory |v 66 |w (DE-604)BV000000970 |9 66 | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Introduction
Chapter 0: Preliminaries
1. Sets and relations 1
2. Topological spaces 5
3. Convergence. Directedness 8
4. Metric spaces 13
5. Spaces of mappings 16
6. Linear topological spaces 19
7. Normed spaces 21
8. Linear operators and functionals 24
9. Conjugate space. Conjugate operator 27
10. Weak topology and reflexivity 29
11. Hilbert spaces 31
Chapter I: Differential calculus in normed spaces
1. The derivate and the differential of a nonlinear operator 35
2. Lagrange formula and Lipschitz condition 39
3. Examples of Frechet differentiable operators 41
4. Lemmas about differentiable operators 43
5. Partial derivatives 45
6. Multilinear operators. Duality. Homogeneous forms 48
7. Higher order derivatives 50
8. Complete continuity of operators and of their derivatives 55
VI
Chapter II: Integration in normed spaces
1. Riemann Stieltjes integrals of vector functions 61
2. Pettis integral and the connection with Riemann Stiltjes integral 65
3. Antiderivatives of vector functions. Integral representations 66
4. Integrals of operators in Banach spaces 71
Chapter III: Holomorphic (analytic) operators and
vector functions on complex Banach spaces
1. Differentiability in complex and real sense.
Cauchy Riemann conditions 76
2. The p topology and holomorphy 80
3. Cauchy integral theorems and their consequences 85
4. Uniqueness theorems and maximum principles
5. Schwartz Lemma and its generalizations 92
6. Uniformly bounded families of p holomorphic (holomorphic) operators.
Montel property 98
Capter IV: Linear operators
1. The spectrum and the resolvent of a linear operator 103
2. Spectral radius 108
3. Resolvent and spectrum of the adjoint operator Ill
4. The spectrum of a completely continuous operator 114
5. Normally solvable operators 117
6. Noether and Fredholm operators 119
7. Projections. Splitable operators 122
8. Invariant subspaces 127
Chapter V: Nonlinear equations with differentiable operators
1. Fixed points. Banach principle 133
2. Non expansive operators 137
3. Fixed points for differentiable operators 143
4. Some applications of fixed point principle 147
5. Implicite and inverse operators. Connection with fixed points 160
Chapter VI: Nonlinear equations with holomorphic operators
1. s fixed points for holomorphic operators.
A converse of Banach principle 171
2. Criterions for the existence of an s fixed point and
its extension with respect to a parameter 177
3. Regular fixed points. Geometric criterions 182
VII
4. Apriori estimates and the extension of an s solution
to the boundary of the domain 189
5. Local inversion of holomorphic operators and
a posteriori error estimates 195
6. Single valued small solutions in some degenerate cases 200
Chapter VII: Banach manifolds
1. Basic definitions 211
2. Smooth mappings 213
3. Submanifolds 214
4. Complex manifolds and Stein manifolds 218
Chapter VIII: Non regular solutions of nonlinear equations
1. Ramification of solutions. Statement of the problem 223
2. Equations of ramification 225
3. Equations of ramification for an analytic operator.
The problem of the coefficients 231
4. The description of the set of fixed points for an
analytic operator 232
Chapter IX: Operators on spaces with indefinite metric
1. Spaces with indefinite metric 239
2. Angle operators 242
3. Plus operators 244
4. Symmetric properties of a plus operator and its adjoint 249
5. The problem of invariant semi definite subspaces 258
6. An application of fixed point principles for
holomorphic operators to the invariant semi definite
subspace problem 262
References 267
List of Symbols 277
Subject Index 279
|
| any_adam_object | 1 |
| author | Khatskevich, Victor Shoiykhet, David 1953- |
| author_GND | (DE-588)1079700099 |
| author_facet | Khatskevich, Victor Shoiykhet, David 1953- |
| author_role | aut aut |
| author_sort | Khatskevich, Victor |
| author_variant | v k vk d s ds |
| building | Verbundindex |
| bvnumber | BV008331936 |
| callnumber-first | Q - Science |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 620 |
| classification_tum | MAT 470f MAT 462f MAT 354f |
| ctrlnum | (OCoLC)29428804 (DE-599)BVBBV008331936 |
| dewey-full | 514/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.72 |
| dewey-search | 514/.72 |
| dewey-sort | 3514 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008331936 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:18:27Z |
| institution | BVB |
| isbn | 3764329297 0817629297 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005504230 |
| oclc_num | 29428804 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-703 DE-739 DE-706 DE-634 DE-11 DE-188 |
| physical | X, 280 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Khatskevich, Victor Verfasser aut Differentiable operators and nonlinear equations Victor Khatskevich ; David Shoiykhet Basel u.a. Birkhäuser 1994 X, 280 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Operator theory 66 Aus dem Russ. übers. Applications différentiables ram Applications holomorphes ram Banach, espaces de ram Niet-lineaire vergelijkingen gtt Operatortheorie gtt Banach spaces Differentiable mappings Holomorphic mappings Holomorphe Abbildung (DE-588)4160471-4 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Differenzierbarkeit (DE-588)4149807-0 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 s Banach-Raum (DE-588)4004402-6 s DE-604 Linearer Operator (DE-588)4167721-3 s Differenzierbarkeit (DE-588)4149807-0 s Nichtlineare Analysis (DE-588)4177490-5 s Shoiykhet, David 1953- Verfasser (DE-588)1079700099 aut Operator theory 66 (DE-604)BV000000970 66 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005504230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khatskevich, Victor Shoiykhet, David 1953- Differentiable operators and nonlinear equations Operator theory Applications différentiables ram Applications holomorphes ram Banach, espaces de ram Niet-lineaire vergelijkingen gtt Operatortheorie gtt Banach spaces Differentiable mappings Holomorphic mappings Holomorphe Abbildung (DE-588)4160471-4 gnd Linearer Operator (DE-588)4167721-3 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4160471-4 (DE-588)4167721-3 (DE-588)4177490-5 (DE-588)4149807-0 (DE-588)4004402-6 |
| title | Differentiable operators and nonlinear equations |
| title_auth | Differentiable operators and nonlinear equations |
| title_exact_search | Differentiable operators and nonlinear equations |
| title_full | Differentiable operators and nonlinear equations Victor Khatskevich ; David Shoiykhet |
| title_fullStr | Differentiable operators and nonlinear equations Victor Khatskevich ; David Shoiykhet |
| title_full_unstemmed | Differentiable operators and nonlinear equations Victor Khatskevich ; David Shoiykhet |
| title_short | Differentiable operators and nonlinear equations |
| title_sort | differentiable operators and nonlinear equations |
| topic | Applications différentiables ram Applications holomorphes ram Banach, espaces de ram Niet-lineaire vergelijkingen gtt Operatortheorie gtt Banach spaces Differentiable mappings Holomorphic mappings Holomorphe Abbildung (DE-588)4160471-4 gnd Linearer Operator (DE-588)4167721-3 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Differenzierbarkeit (DE-588)4149807-0 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Applications différentiables Applications holomorphes Banach, espaces de Niet-lineaire vergelijkingen Operatortheorie Banach spaces Differentiable mappings Holomorphic mappings Holomorphe Abbildung Linearer Operator Nichtlineare Analysis Differenzierbarkeit Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005504230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT khatskevichvictor differentiableoperatorsandnonlinearequations AT shoiykhetdavid differentiableoperatorsandnonlinearequations |