On Ambarzumyan-type theorems
type: Item
instance of: scholarly article
title: On Ambarzumyan-type theorems
zbMATH Open document ID: 1271.34019
published in: Applied Mathematics Letters
publication date: 2013-03-07T00:00:00Z
review text: Let \(\ell\) be a self-adjoint lower semi-bounded linear ordinary differential operator with only discrete spectrum, say \(\lambda_0\leq\lambda_1\leq\dots\). Set \(\tilde{\ell}y+\hat{q}y=\ell y\) for \(\hat{q}\in L_1\) and \(y\) in the domain of \(\ell\). Denoting the spectrum of \(\tilde{\ell}\) by \(\tilde{\lambda}_0\leq\tilde{\lambda}_1\leq\dots\). If \(\tilde{y}_0\) is a normalized eigenfunction to the eigenvalue \(\tilde{\lambda}_0\) of \(\tilde{\ell}\) and \(\lambda_0=\tilde{\lambda}_0+(\hat{q}\tilde{y}_0,\tilde{y}_0)\), then, in this paper, it is shown that \(\hat{q}=\lambda_0-\tilde{\lambda}_0\) a.e. Applications are given.
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 6142824
zbMATH Keywords: Sturm-Liouville
zbMATH Keywords: inverse problems
author: V. A. Yurko
reviewed by: Bruce A. Watson
MaRDI profile type: Publication
full work available at URL: j.aml.2012.12.006
OpenAlex ID: W2015157625
DOI: 10.1016/J.AML.2012.12.006
description: scientific article; zbMATH DE number 6142824