Dissipative eigenvalue problems for a singular Dirac system
type: Item
instance of: scholarly article
title: Dissipative eigenvalue problems for a singular Dirac system
zbMATH Open document ID: 1062.34095
DOI: 10.1016/S0096-3003(03)00550-2
author: Bilender P. Allahverdiev
published in: Applied Mathematics and Computation
publication date: 2004-09-24T00:00:00Z
review text: Lax-Phillips scattering theory and Nagy-Foias' theory of functional models are used for the study of the spectral properties of maximal dissipative extensions of the minimal operator \(L_{0}\) generated by the differential expression \(l(y)=-y''(x)+Q(x)y(x)\) on \((-\infty,\infty)\). The matrix \(Q(x)\) is symmetric and its elements are real-valued and locally integrable on the real line. The author proves that almost all the maximal dissipative extensions of \(L_0\) have purely discrete spectrum included in the open upper half plane and that the system of eigenvectors and associated vectors of these extensions is complete.
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 47B44
Mathematics Subject Classification ID: 47A20
Mathematics Subject Classification ID: 34L25
zbMATH DE Number: 2102860
zbMATH Keywords: Dirac systems
zbMATH Keywords: maximal dissipative operator
zbMATH Keywords: selfadjoint dilation
zbMATH Keywords: characteristic function
zbMATH Keywords: eigenvalue problem
MaRDI profile type: Publication
cites work: Discrete and continuous boundary problems
cites work: The Dirac equation with an anomalous magnetic moment
cites work: Spectral properties of the Dirac equation with anomalous magnetic moment
cites work: The Asymptotic Form of the Titchmarsh-Weyl Coefficient for Dirac Systems
cites work: Hamiltonian systems of limit point or limit circle type with both endpoints singular
cites work: Dirac Systems with Discrete Spectra
cites work: On the number of eigenvalues in the spectral gap of a Dirac system
cites work: A limit-point criterion for separated Dirac operators and a little known result on Riccati's equation
cites work: Q4862628
cites work: Q5616408
cites work: Q4040163
cites work: Q5539945
cites work: Spectra for a Pair of Singular First Order Differential Equations
cites work: Three spectral theorems for a pair of singular first-order differential equations
cites work: Spectral Theory of Dirac's Radial Relativistic Wave Equation
cites work: Some Eigenfunction Expansion Formulae
cites work: ON THE NATURE OF THE SPECTRUM IN PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS
cites work: ON THE NATURE OF THE SPECTRUM IN PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS (II)
cites work: ON THE NATURE OF THE SPECTRUM IN PROBLEMS OF RELATIVISTIC QUANTUM MECHANICS (III)
cites work: Spectral theory of ordinary differential operators
description: scientific article; zbMATH DE number 2102860