Characteristic Functions and Models of Nonself-Adjoint Operators by A. KuzhelCharacteristic Functions and Models of Nonself-Adjoint Operators by A. Kuzhel

Characteristic Functions and Models of Nonself-Adjoint Operators

byA. Kuzhel

Paperback | September 27, 2011

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This work aims to give a systematic presentation of methods used in the spectral theory of non-selfadjoint, generally unbounded, operators. Subjects treated include the wide class of both selfadjoint and non-selfadjoint extensions of Hermitian operators; characteristic functions of a regular extension; the construction of some operator models for different classes of non-selfadjoint operators; the construction of the selfadjoint dilation of an arbitrary dissipative operator and J-unitary and J-selfadjoint dilations of linear operators; the abstract Lax Phillips scheme in scattering theory for spaces with indefinite metric (Pontryagin spaces); the relation between scattering matrix and the characteristic function of J-nonexpansive operators; a structure of J-nonexpansive operators; and contractions and their triangulation. Audience: This book will be of interest to post-graduate students and researchers in the field of functional analysis.
Title:Characteristic Functions and Models of Nonself-Adjoint OperatorsFormat:PaperbackDimensions:254 pagesPublished:September 27, 2011Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401065667

ISBN - 13:9789401065665


Table of Contents

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.