Inverse problem for interior spectral data of the Dirac operator on a finite interval
type: Item
instance of: scholarly article
title: Inverse problem for interior spectral data of the Dirac operator on a finite interval
zbMATH Open document ID: 1021.34073
author: K. Mochizuki
author: I. Trooshin
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2003-02-04T00:00:00Z
review text: The authors consider the Dirac operator, generated by the differential expression \[ l(y)=By'+Qy, \quad 0\leq x\leq 1, \] with \[ B=\begin{pmatrix} 0 & 1 \cr -1 & 0 \end{pmatrix}, \quad Q(x)=\begin{pmatrix} p(x) & q(x) \cr q(x) & -p(x)\end{pmatrix}, \quad y(x)=\begin{pmatrix} y_1(x) \cr y_2(x)\end{pmatrix}, \] subject to the boundary conditions \[ y_1(0)\cos\alpha+y_2(0)\sin\alpha=0,\quad \alpha \in[0,\pi),\quad y_1(1)\cos\beta+y_2(1)\sin\beta=0,\quad \beta\in[0,\pi). \] The authors prove uniqueness theorems taking the spectrum and the set of values of the eigenfunctions at some interior point as the given data.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 1833281
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: Borg theorem
zbMATH Keywords: boundary conditions
zbMATH Keywords: Dirac operator
reviewed by: V. Pivovarchik
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145476343
OpenAlex ID: W2001867520
cites work: Isospectral Dirac operators
cites work: Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
cites work: Q5553587
cites work: An Inverse Sturm–Liouville Problem with Mixed Given Data
cites work: Q5531193
cites work: Q3836490
cites work: Inverse problem for interior spectral data of the Sturm-Liouville operator
cites work: Q4511055
DOI: 10.2977/PRIMS/1145476343
description: scientific article; zbMATH DE number 1833281