Stability of direct and inverse scattering problems for the self-adjoint Schrödinger operators on the half-line
type: Item
instance of: scholarly article
title: Stability of direct and inverse scattering problems for the self-adjoint Schrödinger operators on the half-line
zbMATH Open document ID: 1467.34090
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2021-06-14T00:00:00Z
review text: The author of this article considers the Schrödinger equation \(-y''(x)+q(x)y(x)=k^2y(x)\) on the half-line (\(y>0\)) with the self-adjoint boundary condition \(y'(0)\sin \theta+y(0)\cos\theta=0\), where \(\theta \in (0,\pi]\), the parameter \(k^2\) is the spectral parameter, and \(q(x)\) is real-valued function satisfying \(\int_0^\infty (1+x)^j|q(x)|\,\mathrm{d}x<\infty\). On the one hand, an estimate for the difference of the reflection coefficients is provided as the difference of the corresponding potentials and the parameters in the coundary conditions. On the other hand, an estimate is given for the difference of the potentials as the difference of the corresponding scattering data.
reviewed by: Andreas Kleefeld
Mathematics Subject Classification ID: 34L25
zbMATH DE Number: 7358780
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: direct scattering problem
zbMATH Keywords: inverse scattering problem
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.jmaa.2021.125217
OpenAlex ID: W3146376974
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DOI: 10.1016/J.JMAA.2021.125217
description: scientific article; zbMATH DE number 7358780