An inverse Sturm-Liouville problem by three spectra
type: Item
instance of: scholarly article
title: An inverse Sturm-Liouville problem by three spectra
zbMATH Open document ID: 0948.34014
DOI: 10.1007/BF01236474
author: V. Pivovarchik
published in: Integral Equations and Operator Theory
publication date: 2000-07-19T00:00:00Z
review text: Let \(\{\lambda_{nj}\}_{n\geq 0}\), \(j=1,2,3\), be the eigenvalues to the boundary value problems \(L_j\) for the Sturm-Liouville equation \[ -y''+q(x)y=\lambda y \] with the boundary conditions \(y(0)=y(a)=0,\) \(y(0)=y(a/2)=0\) and \(y(a/2)=y(a)=0\), respectively. Under additional restrictions on the spectra the author studies the inverse problem of recovering \(q\) from the given three spectra \(\{\lambda_{nj}\}_{n\geq 0}\), \(j=1,2,3,\) and provide sufficient conditions for the solvability of this inverse problem.
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34L20
zbMATH DE Number: 1333095
zbMATH Keywords: Sturm-Liouville equation
zbMATH Keywords: inverse spectral problem
reviewed by: V. A. Yurko
MaRDI profile type: Publication
cites work: Q5820676
cites work: Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum
cites work: Discontinuous inverse eigenvalue problems
cites work: An Inverse Sturm–Liouville Problem with Mixed Given Data
cites work: Q3695595
cites work: Q5521760
cites work: Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
description: scientific article; zbMATH DE number 1333095