Overview

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. The concept of regular extensions of an Hermitian (non-densely defined) operator was introduced by A. Kuzhel in 1980. This concept is a natural generalization of proper extensions of symmetric (densely defined) operators. The use of regular extensions enables one to study various classes of extensions of Hermitian operators without using the method of linear relations. The central question in this monograph is to what extent the Hermitian part of a linear operator determines its properties. Various properties are investigated and some applications of the theory are given. Chapter 1 deals with some results from operator theory and the theory of extensions. Chapter 2 is devoted to the investigation of regular extensions of Hermitian (symmetric) operators with certain restrictions. In chapter 3 regular extensions of Hermitian operators with the use of boundary-value spaces are investigated. In the final chapter, the results from chapters 1-3 are applied to the investigation of quasi-differential operators and models of zero-range potential with internal structure.

Full Product Details

Author:   A.V. Kuzhel ,  S.A. Kuzhel
Publisher:   Brill
Imprint:   VSP International Science Publishers
Weight:   0.590kg
ISBN:  

9789067642941

ISBN 10:   9067642940
Pages:   274
Publication Date:   November 1998
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Preface CHAPTER 1: REGULAR EXTENSIONS Linear Operators Spectrum of a Linear Operator Hermitian Operators Symmetric Operators Regular Extensions of Hermitian Operators Dissipative Extensions of Hermitian Operators Accretive Operators CHAPTER 2: REGULAR EXTENSIONS WITH RESTRICTIONS Self-Adjoint Bound-Preserving Extensions of Semibounded Symmetric Operators. Theorem and Hypothesis of Von Neumann Proof of the Von Neumann Hypothesis (Friedrichs Method) Self-Adjoint Norm-Preserving Extensions of Hermitian Contractions Normal Norm-Preserving Extensions of Hermitian Contractions Krein's Proof of the Von Neumann Hypothesis Squared Symmetric Operators Self-Adjoint Bound-Preserving Extensions of Semibounded Hermitian Operators Regular U-Invariant Extensions of Hermitian Operators Canonical Dissipative Extensions of Hermitian Operators CHAPTER 3: BOUNDARY-VALUE SPACES OF HERMITIAN OPERATORS Definition and General Properties of Boundary-Value Spaces Description of Regular-Extensions of Hermitian Operators in Terms of Boundary-Value Spaces Characteristic Functions of Hermitian Operators Spectral Properties of Regular Extensions CHAPTER 4: EXAMPLES AND APPLICATIONS Quasidifferential Operators Boundary-Value Spaces for Model of Zero-Range Potentials with Internal Structure Some Properties of Nonperturbed Operators Abstract Wave Equation Elements of the Lax-Phillips Scattering Theory for -Perturbed Abstract Wave Equation References Subject Index Notation

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