Characteristic Functions and Models of Nonself-Adjoint Operators

Name: Characteristic Functions and Models of Nonself-Adjoint Operators
Brand: Springer
SKU: 9789401065665
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ISBN13: 9789401065665
Binding: Paperback
Subject: N/A
Publisher: Springer
Publisher Imprint: Springer
Publication Date: September 27, 2011
Pages: 254
Original Price: EUR 49.99
Language: English
Edition: Softcover Repri
Item Weight: 468 grams
BISAC Subject(s): Calculus, Algebra / Linear, and Mathematical Analysis

About The Book

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).

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