Two-dimensional trace-normed canonical systems of differential equations and selfadjoint interface conditions
type: Item
instance of: scholarly article
title: Two-dimensional trace-normed canonical systems of differential equations and selfadjoint interface conditions
zbMATH Open document ID: 1092.34007
author: Henrik Winkler
author: H. S. V. de Snoo
published in: Integral Equations and Operator Theory
publication date: 2005-04-21T00:00:00Z
review text: The paper deals with the system \(Jf'=-zH(x)f\) on the line, where \(z\) is a complex parameter, \(H(x)\) is a real, nonnegative \(2\times 2\)-matrix with \(\operatorname{tr} H(x)=1\), and \[ J=\left( \begin{matrix} 0 & -1 \\ 1 & 0 \end{matrix}\right). \] The system is considered with selfadjoint interface conditions at zero. It is shown that the generalized Fourier transforms on \(\mathbb R_{\pm}\) are partially isometric. Compression to the halfline \((0,\infty)\) results in boundary conditions which depend on the eigenvalue parameter involving a fractional linear transform of the Titchmarsh-Weyl coefficient of the halfline \((0,\infty)\). The corresponding generalized Fourier transforms are isometric except possibly on a one-dimensional subspace where they are contractive.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 47A57
zbMATH DE Number: 2160359
zbMATH Keywords: Canonical system
zbMATH Keywords: Titchmarsh-Weyl coefficient
zbMATH Keywords: Fourier transform
zbMATH Keywords: spectral matrix
reviewed by: V. A. Yurko
MaRDI profile type: Publication
full work available at URL: s00020-003-1243-y
OpenAlex ID: W2102095170
DOI: 10.1007/S00020-003-1243-Y
description: scientific article; zbMATH DE number 2160359