Theory of commuting nonselfadjoint operators:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1995
|
| Series: | Mathematics and its applications
332 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 313 S. |
| ISBN: | 0792335880 |
Staff View
MARC
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| 245 | 1 | 0 | |a Theory of commuting nonselfadjoint operators |c by M. S. Livšic ... |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1995 | |
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Record in the Search Index
| _version_ | 1804124857921699840 |
|---|---|
| adam_text | Contents
Preface ix
Introduction xi
I OPERATOR VESSELS IN HILBERT SPACE 1
1 PRELIMINARY RESULTS 3
1.1 Diagonal Matrices 3
1.2 Partial Differential Equations 5
1.3 Algebraic Equations 8
1.4 Examples 15
2 COLLIGATIONS AND VESSELS 18
2.1 Operator Colligations 18
2.2 Colligations of the Second Order 21
2.3 Operator Vessels 22
2.4 Decompositions and Couplings 25
3 OPEN SYSTEMS AND OPEN FIELDS 29
3.1 Open Systems 29
3.2 Open Fields 31
3.3 Adjoint Vessels 34
3.4 Characteristic Functions 36
4 THE GENERALIZED CAYLEY HAMILTON THEOREM 42
4.1 The Discriminant Varieties 42
4.2 Pairs of Operators 45
4.3 The Joint Characteristic Function 49
4.4 One Dimensional Vessels 51
4.5 Vessels and Wave Equations 53
4.6 The Wave Corpuscle Duality 60
4.7 Real Parts of Commuting Nonselfadjoint Operators 67
Notes 70
v
vi
II JOINT SPECTRUM AND DISCRIMINANT VARI¬
ETIES OF A COMMUTATIVE VESSEL 71
5 JOINT SPECTRUM AND THE SPECTRAL MAPPING THEO¬
REM 73
5.1 Definition and the Simplest Properties of Joint Spectra 73
5.2 Spectral Mapping Theorem 76
6 JOINT SPECTRUM OF COMMUTING OPERATORS WITH
COMPACT IMAGINARY PARTS 81
6.1 Some Auxiliary Statements 81
6.2 Joint Spectra and Spectra of Linear Combinations of Operators ... 83
6.3 Coincidence of the Left and the Right Joint Spectra 86
6.4 Joint Spectra and Spectra of Linear Combinations of Operators (Con¬
tinued). Domain of the Joint Characteristic Function 87
7 PROPERTIES OF DISCRIMINANT VARIETIES OF A COMMU¬
TATIVE VESSEL 92
7.1 Non emptiness of Discriminant Varieties 92
7.2 Relation between the Subspaces Ein(z) and Eotit(z) 93
7.3 Relation between the Varieties Din and D°ut 95
Notes 100
III OPERATOR VESSELS IN BANACH SPACES 101
8 OPERATOR COLLIGATIONS AND VESSELS IN BANACH
SPACE 103
8.1 Operator Colligations and Operator Vessels 103
8.2 Discriminant Varieties. Discriminant Ideals. Generalization of the
Cayley Hamilton Theorem Ill
8.3 Decomposition and Coupling of Vessels and Colligations 118
8.4 The Joint Characteristic Function of a Commutative Vessel 124
9 BEZOUTIAN VESSELS IN BANACH SPACE 131
9.1 Resultants, Bezoutiants and Rational Curves 131
9.2 Operator Vessels with Rational Operator Functions 143
9.3 Liiroth Operator Vessels 158
9.4 Coupling of Bezoutian Vessels 171
Notes 184
vii
IV SPECTRAL ANALYSIS OF TWO OPERATOR
VESSELS 185
10 CHARACTERISTIC FUNCTIONS OF TWO OPERATOR VES¬
SELS IN A HILBERT SPACE 187
10.1 The Inverse Problem for Two Operator Vessels 187
10.2 Characteristic Function and Triangular Models for a Single Operator
Colligation 190
10.3 Joint Characteristic Function and the Restoration Formula 199
10.4 Description of the Class of Complete Characteristic Functions .... 204
10.5 Properties of the Joint Characteristic Function 218
11 THE DETERMINANTAL REPRESENTATIONS AND THE
JOINT CHARACTERISTIC FUNCTIONS IN THE CASE OF
REAL SMOOTH CUBICS 234
11.1 Selfadjoint Determinantal Representations of Real Smooth Cubics . . 234
11.2 Definition and Description of Normalized Joint Characteristic
Functions 242
11.3 Properties of Semiexpansive Functions 249
12 TRIANGULAR MODELS FOR COMMUTATIVE TWO
OPERATOR VESSELS ON REAL SMOOTH CUBICS 256
12.1 One Dimensional Vessels and Their Characteristic Functions 256
12.2 Finite Dimensional Triangular Models 261
12.3 Infinite Dimensional Triangular Models: Discrete Case 268
12.4 Infinite Dimensional Triangular Models: Continuous Case 280
Notes 301
References 303
Index 307
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:20Z |
| institution | BVB |
| isbn | 0792335880 |
| language | English |
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| owner_facet | DE-12 DE-824 DE-11 |
| physical | XVI, 313 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Theory of commuting nonselfadjoint operators by M. S. Livšic ... Dordrecht [u.a.] Kluwer 1995 XVI, 313 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 332 Opérateurs non auto-adjoints ram Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd rswk-swf Nichtselbstadjungierter Operator (DE-588)4405912-7 s DE-604 Lîfšîṣ, Moše S. 1917-2007 Sonstige (DE-588)118868012 oth Mathematics and its applications 332 (DE-604)BV008163334 332 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006947063&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Theory of commuting nonselfadjoint operators Mathematics and its applications Opérateurs non auto-adjoints ram Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd |
| subject_GND | (DE-588)4405912-7 |
| title | Theory of commuting nonselfadjoint operators |
| title_auth | Theory of commuting nonselfadjoint operators |
| title_exact_search | Theory of commuting nonselfadjoint operators |
| title_full | Theory of commuting nonselfadjoint operators by M. S. Livšic ... |
| title_fullStr | Theory of commuting nonselfadjoint operators by M. S. Livšic ... |
| title_full_unstemmed | Theory of commuting nonselfadjoint operators by M. S. Livšic ... |
| title_short | Theory of commuting nonselfadjoint operators |
| title_sort | theory of commuting nonselfadjoint operators |
| topic | Opérateurs non auto-adjoints ram Nichtselbstadjungierter Operator (DE-588)4405912-7 gnd |
| topic_facet | Opérateurs non auto-adjoints Nichtselbstadjungierter Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006947063&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT lifsismoses theoryofcommutingnonselfadjointoperators |