Operator functions and localization of spectra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2003
|
| Schriftenreihe: | Lecture notes in mathematics
1830 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 256 S. |
| ISBN: | 3540202463 |
Internformat
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| 100 | 1 | |a Gil', Michail I. |d 1941- |e Verfasser |0 (DE-588)128577916 |4 aut | |
| 245 | 1 | 0 | |a Operator functions and localization of spectra |c Michael I. Gil' |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XIV, 256 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 1830 | |
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| 650 | 7 | |a Análise funcional |2 larpcal | |
| 650 | 7 | |a Lineaire operatoren |2 gtt | |
| 650 | 7 | |a Operadores |2 larpcal | |
| 650 | 7 | |a Opérateur linéaire |2 rasuqam | |
| 650 | 4 | |a Opérateurs linéaires | |
| 650 | 4 | |a Opérateurs, Théorie des | |
| 650 | 4 | |a Perturbation (Mathématiques) | |
| 650 | 7 | |a Perturbation (Mathématiques) |2 rasuqam | |
| 650 | 4 | |a Résolvantes | |
| 650 | 7 | |a Spectraaltheorie |2 gtt | |
| 650 | 4 | |a Spectre (Mathématiques) | |
| 650 | 7 | |a Storingsrekening |2 gtt | |
| 650 | 7 | |a Théorie des opérateurs |2 rasuqam | |
| 650 | 7 | |a Théorie spectrale |2 rasuqam | |
| 650 | 4 | |a Linear operators | |
| 650 | 4 | |a Operator theory | |
| 650 | 4 | |a Perturbation (Mathematics) | |
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| 650 | 4 | |a Spectral theory (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804130350072332288 |
|---|---|
| adam_text | Table of Contents
1. Preliminaries 1
1.1 Vector and Matrix Norms 1
1.2 Classes of Matrices 2
1.3 Eigenvalues of Matrices 3
1.4 Matrix Valued Functions 4
1.5 Contour Integrals 5
1.6 Algebraic Equations 6
1.7 The Triangular Representation of Matrices 7
1.8 Notes 8
References 8
2. Norms of Matrix Valued Functions 11
2.1 Estimates for the Euclidean Norm of the Resolvent 11
2.2 Examples 13
2.3 Relations for Eigenvalues 14
2.4 An Auxiliary Inequality 17
2.5 Euclidean Norms of Powers of Nilpotent Matrices 18
2.6 Proof of Theorem 2.1.1 20
2.7 Estimates for the Norm
of Analytic Matrix Valued Functions 21
2.8 Proof of Theorem 2.7.1 22
2.9 The First Multiplicative Representation of the Resolvent ... 24
2.10 The Second Multiplicative Representation of the Resolvent . 27
2.11 The First Relation between Determinants and Resolvents . . 28
2.12 The Second Relation between Determinants and Resolvents . 30
2.13 Proof of Theorem 2.12.1 30
2.14 An Additional Estimate for Resolvents 32
2.15 Notes 33
References 33
3. Invertibility of Finite Matrices 35
3.1 Preliminary Results 35
3.2 /P Norms of Powers of Nilpotent Matrices 37
X Table of Contents
3.3 Invertibility in the Norm ||.||p (1 p oo) 39
3.4 Invertibility in the Norm jj.jjoo 40
3.5 Proof of Theorem 3.4.1 41
3.6 Positive Invertibility of Matrices 44
3.7 Positive Matrix Valued Functions 45
3.8 Notes 47
References 47
4. Localization of Eigenvalues of Finite Matrices 49
4.1 Definitions and Preliminaries 49
4.2 Perturbations of Multiplicities and Matching Distance .... 50
4.3 Perturbations of Eigenvectors and Eigenprojectors 52
4.4 Perturbations of Matrices in the Euclidean Norm 53
4.5 Upper Bounds for Eigenvalues in Terms
of the Euclidean Norm 56
4.6 Lower Bounds for the Spectral Radius 57
4.7 Additional Bounds for Eigenvalues 59
4.8 Proof of Theorem 4.7.1 60
4.9 Notes 62
References 62
5. Block Matrices and n Triangular Matrices 65
5.1 Invertibility of Block Matrices 65
5.2 7T Triangular Matrices 67
5.3 Multiplicative Representation of Resolvents
of 7r Triangular Operators 69
5.4 Invertibility with Respect to a Chain of Projectors 70
5.5 Proof of Theorem 5.1.1 72
5.6 Notes 74
References 74
6. Norm Estimates for Functions of Compact Operators
in a Hilbert Space 75
6.1 Bounded Operators in a Hilbert Space 75
6.2 Compact Operators in a Hilbert Space 77
6.3 Triangular Representations of Compact Operators 79
6.4 Resolvents of Hilbert Schmidt Operators 83
6.5 Equalities for Eigenvalues of a Hilbert Schmidt Operator ... 84
6.6 Operators Having Hilbert Schmidt Powers 86
6.7 Resolvents of Neumann Schatten Operators 88
6.8 Proofs of Theorems 6.7.1 and 6.7.3 88
6.9 Regular Functions of Hilbert Schmidt Operators 91
6.10 A Relation between Determinants and Resolvents 93
6.11 Notes 95
References 95
Table of Contents XI
7. Functions of Non compact Operators 97
7.1 Terminology 97
7.2 P Triangular Operators 98
7.3 Some Properties of Volterra Operators 99
7.4 Powers of Volterra Operators 100
7.5 Resolvents of P Triangular Operators 101
7.6 Triangular Representations of Quasi Hermitian Operators . . 104
7.7 Resolvents of Operators
with Hilbert Schmidt Hermitian Components 106
7.8 Operators with the Property Av (A*)v £ C2 107
7.9 Resolvents of Operators
with Neumann Schatten Hermitian Components 108
7.10 Regular Functions of Bounded Quasi Hermitian Operators . 109
7.11 Proof of Theorem 7.10.1 110
7.12 Regular Functions of Unbounded Operators 113
7.13 Triangular Representations of Regular Functions 115
7.14 Triangular Representations of Quasiunitary Operators .... 116
7.15 Resolvents and Analytic Functions
of Quasiunitary Operators 117
7.16 Notes 120
References 120
8. Bounded Perturbations of Nonselfadjoint Operators 123
8.1 Invertibility of Boundedly Perturbed
P Triangular Operators 123
8.2 Resolvents of Boundedly Perturbed
P Triangular Operators 126
8.3 Roots of Scalar Equations 127
8.4 Spectral Variations 129
8.5 Perturbations of Compact Operators 130
8.6 Perturbations of Operators
with Compact Hermitian Components 132
8.7 Notes 134
References 134
9. Spectrum Localization of Nonself adjoint Operators 135
9.1 Invertibility Conditions 135
9.2 Proofs of Theorems 9.1.1 and 9.1.3 137
9.3 Resolvents of Quasinormal Operators 139
9.4 Upper Bounds for Spectra 142
9.5 Inner Bounds for Spectra 143
9.6 Bounds for Spectra of Hilbert Schmidt Operators 145
9.7 Von Neumann Schatten Operators 146
9.8 Operators with Hilbert Schmidt Hermitian Components . . . 147
9.9 Operators with Neumann Schatten Hermitian Components . 148
XII Table of Contents
9.10 Notes 149
References 149
10. Multiplicative Representations of Resolvents 151
10.1 Operators with Finite Chains of Invariant Projectors 151
10.2 Complete Compact Operators 154
10.3 The Second Representation for Resolvents
of Complete Compact Operators 156
10.4 Operators with Compact Inverse Ones 157
10.5 Multiplicative Integrals 158
10.6 Resolvents of Volterra Operators 159
10.7 Resolvents of P Triangular Operators 159
10.8 Notes 161
References 161
11. Relatively P Triangular Operators 163
11.1 Definitions and Preliminaries 163
11.2 Resolvents of Relatively P Triangular Operators 165
11.3 Invertibility of Perturbed RPTO 166
11.4 Resolvents of Perturbed RPTO 167
11.5 Relative Spectral Variations 167
11.6 Operators with von Neumann Schatten Relatively
Nilpotent Parts 168
11.7 Notes 172
References 172
12. Relatively Compact Perturbations of Normal Operators 173
12.1 Invertibility Conditions 173
12.2 Estimates for Resolvents 175
12.3 Bounds for the Spectrum 176
12.4 Operators with Relatively von Neumann Schatten
Off diagonal Parts 177
12.5 Notes 180
References 180
13. Infinite Matrices in Hilbert Spaces
and Differential Operators 181
13.1 Matrices with Compact off Diagonals 181
13.2 Matrices with Relatively Compact Off diagonals 184
13.3 A Nonselfadjoint Differential Operator 185
13.4 Integro differential Operators 186
13.5 Notes 187
References 188
Table of Contents XIII
14. Integral Operators in Space L2 189
14.1 Scalar Integral Operators 189
14.2 Matrix Integral Operators with Relatively Small Kernels . . . 191
14.3 Perturbations of Matrix Convolutions 193
14.4 Notes 196
References 197
15. Operator Matrices 199
15.1 Invertibility Conditions 199
15.2 Bounds for the Spectrum 202
15.3 Operator Matrices with Normal Entries 204
15.4 Operator Matrices with Bounded off Diagonal Entries .... 205
15.5 Operator Matrices with Hilbert Schmidt Diagonal Operators 207
15.6 Example 209
15.7 Notes 212
References 212
16. Hille Tamarkin Integral Operators 215
16.1 Invertibility Conditions 215
16.2 Preliminaries 217
16.3 Powers of Volterra Operators 219
16.4 Spectral Radius of a Hille Tamarkin Operator 221
16.5 Nonnegative Invertibility 222
16.6 Applications 223
16.7 Notes 226
References 226
17. Integral Operators in Space L°° 227
17.1 Invertibility Conditions 227
17.2 Proof of Theorem 17.1.1 228
17.3 The Spectral Radius 230
17.4 Nonnegative Invertibility 231
17.5 Applications 232
17.6 Notes 234
References 234
18. Hille Tamarkin Matrices 235
18.1 Invertibility Conditions 235
18.2 Proof of Theorem 18.1.1 237
18.3 Localization of the Spectrum 238
18.4 Notes 240
References 241
XIV Table of Contents
19. Zeros of Entire Functions 243
19.1 Perturbations of Zeros 243
19.2 Proof of Theorem 19.1.2 246
19.3 Bounds for Sums of Zeros 248
19.4 Applications of Theorem 19.3.1 250
19.5 Notes 252
References 252
List of Main Symbols 253
Index 255
|
| any_adam_object | 1 |
| author | Gil', Michail I. 1941- |
| author_GND | (DE-588)128577916 |
| author_facet | Gil', Michail I. 1941- |
| author_role | aut |
| author_sort | Gil', Michail I. 1941- |
| author_variant | m i g mi mig |
| building | Verbundindex |
| bvnumber | BV017589355 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 620 |
| classification_tum | MAT 472f |
| ctrlnum | (OCoLC)53223749 (DE-599)BVBBV017589355 |
| dewey-full | 515/.7246 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515/.7246 510 |
| dewey-search | 515/.7246 510 |
| dewey-sort | 3515 47246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017589355 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:19:38Z |
| institution | BVB |
| isbn | 3540202463 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010582317 |
| oclc_num | 53223749 |
| open_access_boolean | |
| owner | DE-824 DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-824 DE-91G DE-BY-TUM DE-20 DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | XIV, 256 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Gil', Michail I. 1941- Verfasser (DE-588)128577916 aut Operator functions and localization of spectra Michael I. Gil' Berlin [u.a.] Springer 2003 XIV, 256 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1830 Análise espectral (análise funcional) larpcal Análise funcional larpcal Lineaire operatoren gtt Operadores larpcal Opérateur linéaire rasuqam Opérateurs linéaires Opérateurs, Théorie des Perturbation (Mathématiques) Perturbation (Mathématiques) rasuqam Résolvantes Spectraaltheorie gtt Spectre (Mathématiques) Storingsrekening gtt Théorie des opérateurs rasuqam Théorie spectrale rasuqam Linear operators Operator theory Perturbation (Mathematics) Resolvents (Mathematics) Spectral theory (Mathematics) Norm Mathematik (DE-588)4172021-0 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Operatorfunktion (DE-588)4202830-9 gnd rswk-swf Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd rswk-swf Spektrum Mathematik (DE-588)4182180-4 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Nichtselbstadjungierter Operator (DE-588)4405912-7 s Spektrum Mathematik (DE-588)4182180-4 s Hilbert-Raum (DE-588)4159850-7 s DE-604 Operatorfunktion (DE-588)4202830-9 s Norm Mathematik (DE-588)4172021-0 s Lecture notes in mathematics 1830 (DE-604)BV000676446 1830 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010582317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gil', Michail I. 1941- Operator functions and localization of spectra Lecture notes in mathematics Análise espectral (análise funcional) larpcal Análise funcional larpcal Lineaire operatoren gtt Operadores larpcal Opérateur linéaire rasuqam Opérateurs linéaires Opérateurs, Théorie des Perturbation (Mathématiques) Perturbation (Mathématiques) rasuqam Résolvantes Spectraaltheorie gtt Spectre (Mathématiques) Storingsrekening gtt Théorie des opérateurs rasuqam Théorie spectrale rasuqam Linear operators Operator theory Perturbation (Mathematics) Resolvents (Mathematics) Spectral theory (Mathematics) Norm Mathematik (DE-588)4172021-0 gnd Linearer Operator (DE-588)4167721-3 gnd Operatorfunktion (DE-588)4202830-9 gnd Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4172021-0 (DE-588)4167721-3 (DE-588)4202830-9 (DE-588)4405912-7 (DE-588)4182180-4 (DE-588)4159850-7 |
| title | Operator functions and localization of spectra |
| title_auth | Operator functions and localization of spectra |
| title_exact_search | Operator functions and localization of spectra |
| title_full | Operator functions and localization of spectra Michael I. Gil' |
| title_fullStr | Operator functions and localization of spectra Michael I. Gil' |
| title_full_unstemmed | Operator functions and localization of spectra Michael I. Gil' |
| title_short | Operator functions and localization of spectra |
| title_sort | operator functions and localization of spectra |
| topic | Análise espectral (análise funcional) larpcal Análise funcional larpcal Lineaire operatoren gtt Operadores larpcal Opérateur linéaire rasuqam Opérateurs linéaires Opérateurs, Théorie des Perturbation (Mathématiques) Perturbation (Mathématiques) rasuqam Résolvantes Spectraaltheorie gtt Spectre (Mathématiques) Storingsrekening gtt Théorie des opérateurs rasuqam Théorie spectrale rasuqam Linear operators Operator theory Perturbation (Mathematics) Resolvents (Mathematics) Spectral theory (Mathematics) Norm Mathematik (DE-588)4172021-0 gnd Linearer Operator (DE-588)4167721-3 gnd Operatorfunktion (DE-588)4202830-9 gnd Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd Spektrum Mathematik (DE-588)4182180-4 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Análise espectral (análise funcional) Análise funcional Lineaire operatoren Operadores Opérateur linéaire Opérateurs linéaires Opérateurs, Théorie des Perturbation (Mathématiques) Résolvantes Spectraaltheorie Spectre (Mathématiques) Storingsrekening Théorie des opérateurs Théorie spectrale Linear operators Operator theory Perturbation (Mathematics) Resolvents (Mathematics) Spectral theory (Mathematics) Norm Mathematik Linearer Operator Operatorfunktion Nichtselbstadjungierter Operator Spektrum Mathematik Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010582317&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT gilmichaili operatorfunctionsandlocalizationofspectra |