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Book Categories |
Introduction | 1 | |
Ch. 1 | Regular Extensions of Hermitian Operators | 3 |
1 | Principal Concepts | 3 |
2 | Auxiliary Operators and Their Application | 13 |
3 | Dissipative Operators | 24 |
Ch. 2 | Characteristic Functions | 33 |
1 | Characteristic Matrix Functions of Regular Extensions | 33 |
2 | A Criterion of Unitary Equivalence | 39 |
3 | Determination of Characteristic Matrix Functions | 42 |
4 | Examples | 50 |
5 | Properties of Characteristic Matrix-Functions | 57 |
6 | Theorem on Multiplication of Characteristic Matrix Functions | 65 |
7 | Factorization of Characteristic Matrix Functions | 75 |
8 | Characteristic Operator Functions | 86 |
9 | Characteristic Functions. Brief Survey | 96 |
Ch. 3 | Models of Nonself-Adjoint Operators | 111 |
1 | Preliminary Remarks | 111 |
2 | K[superscript r]-Operators with Real Spectrum | 112 |
3 | K[superscript r]-Operators with Spectrum Concentrated at Infinity | 128 |
4 | K[superscript r]-Operators with Discrete Spectrum | 131 |
5 | General Case | 147 |
6 | Models of Linear Operators (A Brief Survey) | 153 |
Ch. 4 | Dilations of Linear Operators | 173 |
1 | A Brief Survey | 173 |
2 | Self-Adjoint Dilation of a Dissipative Operator (First Method) | 174 |
3 | Symmetric and Self-Adjoint Dilations of Dissipative Operators (Second Method) | 184 |
4 | J-Unitary and J-Selfadjoint Dilations | 190 |
5 | Coordinate-Free Form of Dilations | 192 |
Appendix 1. Contractions. Triangulation of Contractions | 195 | |
Appendix 2. The Structure of J-Nonexpanding Operators | 206 | |
Appendix 3. Lax-Phillips Abstract Scattering Scheme in Pontryagin Spaces | 217 | |
References | 251 | |
Subject Index | 269 | |
Author Index | 271 | |
Notation | 273 |
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