Remarks on a paper of Kotani concerning generalized reflectionless Schrödinger potentials
type: Item
instance of: scholarly article
title: Remarks on a paper of Kotani concerning generalized reflectionless Schrödinger potentials
zbMATH Open document ID: 1204.37016
author: Luca Zampogni
author: Russell Johnson
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2010-09-22T00:00:00Z
review text: Within the class \({\mathcal R}\) of generalized reflectionless Schrödinger potentials various results are proved. Given a Schrödinger operator \[ L=-\frac{d^2}{dx^2}+q(x) \] with \(q\in{\mathcal R}\), there corresponds a regular Borel measure \(\sigma\) which is supported on a finite symmetric subinterval of \(\mathbb R\). The first goal of the paper is to study the correspondence \(q\to\sigma\) in the case when \(q\) is a generic element of a ``stationary ergodic process'' \(Q\subset{\mathcal R}\). The second goal relates the so-called Marchenko-Lundina class \({\mathcal R}\) to another class which consists, roughly speaking, of real-valued Schrödinger potentials \(q\) which are of limit point type \(\pm\infty\) in the classical Weyl terminology, and which are also of Sato-Segal-Wilson type. Finally, some facts regarding the Floquet exponent of a stationary ergodic process \(Q\subset{\mathcal R}\) are discussed.
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 5790146
zbMATH Keywords: generalized reflectionless potential
zbMATH Keywords: Sato-Segal-Wilson potential
zbMATH Keywords: stationary ergodic process
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
full work available at URL: dcdsb.2010.14.559
OpenAlex ID: W2016227732
DOI: 10.3934/DCDSB.2010.14.559
description: scientific article; zbMATH DE number 5790146