A complete spectral characterization of the double commutation method
type: Item
instance of: scholarly article
title: A complete spectral characterization of the double commutation method
zbMATH Open document ID: 0813.34074
published in: Journal of Functional Analysis
publication date: 1994-01-13T00:00:00Z
review text: The Schrödinger operator \(-d^ 2/dx^ 2 + V(x)\) on the line \(\mathbb{R}\) or on the halfline \((0, \infty)\) and auxiliary operators which appear in the framework of the double commutation method (as a composition of two first order operators) are considered. A complete spectral characterization of the method which introduces eigenvalues into arbitrary spectral gaps of the Schrödinger operator is provided. The main result is unitary equivalence of the double commuted operator, restricted to the orthogonal complement of the eigenspace corresponding to the newly inserted eigenvalues, with the original background operator.
reviewed by: S.L.Edelstein
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 483973
zbMATH Keywords: factorization
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: double commutation method
zbMATH Keywords: spectral characterization
zbMATH Keywords: eigenvalues
author: Fritz Gesztesy
MaRDI profile type: Publication
full work available at URL: jfan.1993.1132
OpenAlex ID: W2080550105
DOI: 10.1006/JFAN.1993.1132
description: scientific article; zbMATH DE number 483973