Characteristic Functions and Models of Nonself-Adjoint Operators

A. Kuzhel

ISBN 10: 9401065667 / ISBN 13: 9789401065665

Published by Springer Netherlands, 2011

About this Item

Druck auf Anfrage Neuware - Printed after ordering - Over the last decades, the study of nonself-adjoint or nonunitary operators has been mainly based on the method of characteristic functions and on methods of model construction or dilatation for corresponding operator classes. The characteristic function is a mathematical object (a matrix or an operator) associated with a class of nonself-adjoint (or nonunitary) operators that describes the spectral properties of the operators from this class. It may happen that characteristic functions are simpler than the corresponding operators; in this case one can significantly simplify the problem under investigation for these operators. For given characteristic function of an operator A, we construct, in explicit form, an operator that serves as a model A of the operator A in a certain linear space (to some extent this resembles the construction of diagonal and triangular matrices' unitary equivalent or similar, to certain matrix classes). The study of this model operator may give much information about the original operator (its spectrum, the completeness of the system of root subspaces, etc.). In this book, we consider various classes of linear (generally speaking, unbounded) operators, construct and study their characteristic functions and models. We also present a detailed study of contractiol)s and dissipative operators (in particular, from the viewpoint of their triangulation).

Seller Inventory # 9789401065665

Bibliographic Details

• Title: Characteristic Functions and Models of Nonself-Adjoint Operators
• Publisher: Springer Netherlands
• Publication Date: 2011
• Language: English
• ISBN 10: 9401065667
• ISBN 13: 9789401065665
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 160H x 16D millimeters 240 millimeters width by 160 millimeters height by 16 millimeters depth
• Weight: 471 grams

About this title

Synopsis

Over the last decades, the study of nonself-adjoint or nonunitary operators has been mainly based on the method of characteristic functions and on methods of model construction or dilatation for corresponding operator classes. The characteristic function is a mathematical object (a matrix or an operator) associated with a class of nonself-adjoint (or nonunitary) operators that describes the spectral properties of the operators from this class. It may happen that characteristic functions are simpler than the corresponding operators; in this case one can significantly simplify the problem under investigation for these operators. For given characteristic function of an operator A, we construct, in explicit form, an operator that serves as a model A of the operator A in a certain linear space (to some extent this resembles the construction of diagonal and triangular matrices' unitary equivalent or similar, to certain matrix classes). The study of this model operator may give much information about the original operator (its spectrum, the completeness of the system of root subspaces, etc.). In this book, we consider various classes of linear (generally speaking, unbounded) operators, construct and study their characteristic functions and models. We also present a detailed study of contractiol)s and dissipative operators (in particular, from the viewpoint of their triangulation).