Spectral problems for canonical systems of equations on the axis
type: Item
instance of: scholarly article
title: Spectral problems for canonical systems of equations on the axis
zbMATH Open document ID: 0913.34068
published in: Russian Journal of Mathematical Physics
publication date: 1999-05-24T00:00:00Z
review text: Direct and inverse spectral problems on the axis \((-\infty, \infty)\) are investigated for the following system of integral equations \[ w(x,z) = E_{2m} + izJ \int_0^x [d\sigma(t)] w(x,z), \] with \(J = \left(\begin{smallmatrix} 0 & E_m\\ E_m & 0\end{smallmatrix}\right)\), \(E_m\) is the identity matrix of order \(m,\) \(\sigma (s)\) is a continuous monotone increasing matrix function of order \(2m \times 2m \) on the segment \([-l, l].\) The problem on the axis is reduced to the problem on the half-axis. Corresponding Weyl-Titchmarsh functions are studied.
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 47A45
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1206246
zbMATH Keywords: direct and inverse spectral problems
zbMATH Keywords: canonical system
zbMATH Keywords: Weyl-Titchmarsh function
author: Lev A. Sakhnovich
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1206246