Half inverse problems for quadratic pencils of Sturm-Liouville operators
type: Item
instance of: scholarly article
title: Half inverse problems for quadratic pencils of Sturm-Liouville operators
zbMATH Open document ID: 1256.34013
author: Chuan-Fu Yang
author: Anton Zettl
published in: Taiwanese Journal of Mathematics
publication date: 2012-11-09T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/2389
review text: The paper deals with boundary value problems for the Sturm-Liouville-type quadratic pencil \[ -y''+[q(x)+2\lambda p(x)]y = \lambda^2 y \] on \((0,\pi)\). First, the authors obtain the asymptotic formulae for the eigenvalues of problems with separated boundary conditions. Second, a uniqueness theorem for a ``half-inverse'' problem of the Hochstadt-Lieberman type is proved. The theorem states that a single spectrum (with fixed boundary conditions at the right end) uniquely determines both \(q\) and \(p\) provided they are given on the right half-interval \([\pi/2,\pi]\). The basic tool is the integral representation of the solution of the initial value problem for the quadratic pencil with kernels independent of the spectral parameter \(\lambda\).
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34B09
zbMATH DE Number: 6103938
zbMATH Keywords: Sturm-Liouville operators
zbMATH Keywords: half-inverse problem
zbMATH Keywords: quadratic pencils
zbMATH Keywords: eigenvalue asymptotics
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
OpenAlex ID: W4247525623
DOI: 10.11650/TWJM/1500406800
description: scientific article; zbMATH DE number 6103938