On Borg-type theorems for first-order systems on a finite interval
type: Item
instance of: scholarly article
title: On Borg-type theorems for first-order systems on a finite interval
zbMATH Open document ID: 0942.34078
DOI: 10.1007/BF02465147
publication date: 2000-08-14T00:00:00Z
review text: It is shown that the \(n\times n\) potential matrix \(Q(x)\) with zero diagonal entries in the first-order system \[ -iBy^\prime(x)+Q(x)y=\lambda y,\qquad 0<x<1, \] with \(B=\text{diag}(\lambda_1I_{n_1},\cdots,\lambda_rI_{n_r})\), \(n_1+\cdots+n_r=n\) and \(\sum_{j=1}^r n_j\text{sgn} \lambda_j=0\), is uniquely determined by its spectra under specified number of linearly independent separated boundary conditions. In particular, for \(n=2n_1\) and \(\lambda_1\lambda_2<0\), \(2n_1^2+1\) spectra suffice; in more general situations the potential \(Q(x)\) is also assumed to have an analytic continuation. Similar results are obtained for the uniqueness of the solution to the inverse spectral problem if the potential is known on part of \([0,1]\) and some spectra are given.
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 1407618
zbMATH Keywords: inverse spectral problem
zbMATH Keywords: monodromy matrix
author: M. M. Malamud
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1407618