Inverse nodal problems of discontinuous Sturm-Liouville operator
type: Item
instance of: scholarly article
title: Inverse nodal problems of discontinuous Sturm-Liouville operator
zbMATH Open document ID: 1267.34033
author: Chuan-Fu Yang
published in: Journal of Differential Equations
publication date: 2013-02-28T00:00:00Z
review text: The paper deals with the Sturm-Liouville equation on a finite interval (namely, on \((0,1)\)), with jump conditions at an internal point of the interval, of the type \[ y(1/2+0)=a_1 y(1/2-0), y'(1/2+0)=a_1^{-1} y'(1/2-0) + a_2 y(1/2-0). \] Supplemented with boundary conditions at the ends of the interval, the equation determines a self-adjoint operator. The author studies the inverse problem consisting in the reconstruction of the operator (i.e., the potential, the constants involved in the boundary conditions, and the jump parameters \(a_1\) and \(a_2\)) from the set of zeros of the eigenfunctions (nodes). He introduces the notions of subnodal set and twin subnodal set and proves that a dense subnodal set determines uniquely the operator (the potential and the parameters). The reconstruction formulas are given and the stability of the reconstruction is discussed.
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 6140139
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: discontinuous condition
zbMATH Keywords: inverse nodal problem
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
full work available at URL: j.jde.2012.11.018
OpenAlex ID: W2108717184
DOI: 10.1016/J.JDE.2012.11.018
description: scientific article; zbMATH DE number 6140139