Singular numbers of a boundary-value problem on the halfline for a linear system of ordinary differential equations
type: Item
instance of: scholarly article
title: Singular numbers of a boundary-value problem on the halfline for a linear system of ordinary differential equations
zbMATH Open document ID: 0697.34029
DOI: 10.1007/BF00971748
author: N. E. Zubov
published in: Siberian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: The singular numbers of a closed linear operator in a Hilbert space with dense domain of definition are defined and their basic properties are derived. Operators connected with the boundary value problems for the systems of differential equations are investigated as well as the singular spectrum. Operators \(T_ 0\in L_ 2(R)\) defined as \(T_ 0y(t):=dy(t)/dt-Ay(t),\) where A denotes an \(n\times n\) matrix without imaginary eigenvalues, and T which complies in addition with the boundary condition \(Ly(0)=0\) are studied in more details. It is proved e.g. that under certain conditions the singular spectrum of \(T_ 0\) or T, respectively, is formed by the halfline \([\sigma_*,\infty)\) or \([\sigma_*,\infty)\) and finite number points, respectively, where \(\sigma_*=\min_{\omega}\sigma_ 1(i\omega I-A),\) \(\delta_ 1(i\omega I-A)\) being the least singular number of the matrix \(i\omega\) I-A.
reviewed by: J.Vosmanský
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 4142486
zbMATH Keywords: singular numbers
zbMATH Keywords: closed linear operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: singular spectrum
MaRDI profile type: Publication
cites work: Q3994639
cites work: Q3026133
cites work: Q3231492
cites work: Q3278549
description: scientific article; zbMATH DE number 4142486