An inverse spectral problem for a nonnormal first order differential operator
type: Item
instance of: scholarly article
title: An inverse spectral problem for a nonnormal first order differential operator
zbMATH Open document ID: 0855.34016
DOI: 10.1007/BF01308627
author: Yanyan Li
published in: Integral Equations and Operator Theory
publication date: 1997-02-16T00:00:00Z
review text: The authors study the eigenvalues of two restrictions of the operator \[ A = \left( \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right) \partial_x + \left( \begin{matrix} r(x) & 0 \\ 0 & g(x) \end{matrix} \right), \] where \(r\) and \(g\) are Lipschitz functions on \([0,1]\). They establish asymptotic formulas for these eigenvalues and show that the corresponding root vectors form a basis in \(L^2 \times L^2\). A related inverse problem was studied by \textit{M. Yamamoto} [J. Fac. Sci. Univ. Tokyo, Sect. IA 35, 519-546 (1988; Zbl 0667.34018)].
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34L20
zbMATH DE Number: 908002
zbMATH Keywords: eigenvalues
zbMATH Keywords: asymptotic formulas
zbMATH Keywords: root vectors
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01308627
OpenAlex ID: W2012146557
description: scientific article; zbMATH DE number 908002