Some remarks concerning the scattering theory for the Sturm-Liouville operator
type: Item
instance of: scholarly article
title: Some remarks concerning the scattering theory for the Sturm-Liouville operator
zbMATH Open document ID: 1495.34118
author: Luca Zampogni
published in: Journal of Dynamics and Differential Equations
publication date: 2022-03-17T00:00:00Z
review text: The author discusses scattering theory for the Sturm-Liouville operator \[ L = \frac {1}{y} \Big( - \frac{d^2}{dx^2} + q \Big), \] which depends on the parameter \(q \in \mathbb C_0(\mathbb R)\) and a strictly positive weight function \(y \in \mathbb C_0(\mathbb R)\), which is assumed to be fixed. A scattering hypothesis on the function \(q\) is given and the set of scattering data is described. The relation between the scattering coefficients and the potential \(q\) is studied, and then used to solve the inverse scattering problem, that is, the reconstruction of \(q\) when \(y\) is fixed and a set of scattering data is given. In addition, several relations concerning the spectral properties of \(L\) and the solutions of the related eigenvalue equation are established.
reviewed by: Johanna Michor
Mathematics Subject Classification ID: 34L25
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 7491611
zbMATH Keywords: inverse problems
zbMATH Keywords: Sturm-Liouville operators
zbMATH Keywords: scattering theory
MaRDI profile type: Publication
full work available at URL: s10884-020-09922-8
OpenAlex ID: W3119286062
Wikidata QID: Q115383329
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DOI: 10.1007/S10884-020-09922-8
description: scientific article; zbMATH DE number 7491611