Uniqueness of the interior transmission problem with partial information on the potential and eigenvalues
type: Item
instance of: scholarly article
title: Uniqueness of the interior transmission problem with partial information on the potential and eigenvalues
zbMATH Open document ID: 1335.34043
author: Chuan-Fu Yang
author: Sergey Buterin
published in: Journal of Differential Equations
publication date: 2016-01-26T00:00:00Z
review text: The paper deals with the boundary value problem \(B(q)\) of the form \[ y''+(\lambda-q(x))y=0, \quad 0<x<1, \quad y(0)=y(1)\cos\sqrt\lambda a-y'(1)\frac{\sin\sqrt\lambda a}{\sqrt\lambda}=0, \] where \(\lambda\) is the spectral parameter, \(q(x)\) is a real-valued function from \(L_2(0,1)\) and the positive parameter \(a\neq1\) is fixed. The authors study the inverse problem of recovering \(q(x)\) from the spectrum of \(B(q).\) In particular, they prove that \(q(x)\) is uniquely determined by a part of the real eigenvalues, provided that on a subinterval \(q(x)\) is known a priori. The connection between the length of this subinterval and the density of the real eigenvalues specified as well as the value of \(a\) is described.
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 6535777
zbMATH Keywords: interior transmission problem
zbMATH Keywords: inverse spectral problem
zbMATH Keywords: Weyl function
reviewed by: V. A. Yurko
MaRDI profile type: Publication
full work available at URL: j.jde.2015.11.031
OpenAlex ID: W2186400331
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DOI: 10.1016/J.JDE.2015.11.031
description: scientific article; zbMATH DE number 6535777