Characteristic Functions and Models of Nonself-Adjoint Operators

Introduction. 1: Regular Extensions of Hermitian Operators. 1. Principal Concepts. 2. Auxiliary Operators and Their Application. 3. Dissipative Operators. 2: Characteristic Functions. 1. Characteristic Matrix Functions of Regular Extensions. 2. A Criterion of Unitary Equivalence. 3. Determination of Characteristic Matrix Functions. 4. Examples. 5. Properties of Characteristic Matrix-Functions. 6. Theorem on Multiplication of Characteristic Matrix Functions. 7. Factorization of Characteristic Matrix Functions. 8. Characteristic Operator Functions. 9. Characteristic Functions. Brief Survey. 3: Models of Nonself-Adjoint Operators. 1. Preliminary Remarks. 2. Kr-Operators with Real Spectrum. 3. Kr-Operators with Spectrum Concentrated at Infinity. 4. Kr-Operators with Discrete Spectrum. 5. General Case. 6. Models of Linear Operators (A Brief Survey). 4: Dilations of Linear Operators. 1. A Brief Survey. 2. Self-Adjoint Dilation of a Dissipative Operator (First Method). 3. Symmetric and Self-Adjoint Dilations of Dissipative Operators (Second Method). 4. J-Unitary and J-Selfadjoint Dilations. 5. Coordinate-Free Form of Dilations. Appendix 1: Contractions. Triangulation of Contractions. Appendix 2: The Structure of J-Nonexpanding Operators. Appendix 3: Lax-Phillips Abstract Scattering Scheme in Pontryagin Spaces. References. Subject Index. Personal Index. Notation. Index.