Reconstruction of pencils of differential operators on the half-line
type: Item
instance of: scholarly article
title: Reconstruction of pencils of differential operators on the half-line
zbMATH Open document ID: 0974.34022
DOI: 10.1007/BF02686257
published in: Mathematical Notes
publication date: 2001-05-13T00:00:00Z
review text: The author deals with the inverse problem of reconstructing the coefficients of the differential pencil \[ ly\equiv y''+(\rho^2+i\rho q_1(x)+q_0(x))y=0,\quad x>0, \] and the linear form \[ U(y)=y'(0)+(i\rho h_1+h_0)y(0), \] where \(q_j \in W_1^j(0,\infty)\) are complex-valued functions and \(h_0, h_1\) are complex numbers, with \(h_1\neq \pm 1\). The Weyl function generated by the pair \(L=(l,U)\) is the main tool. New qualitative effects typical for pencils of differential operators are discovered. As a particular case, the inverse problem for the wave equation can be reduced to the inverse spectral problem for the above pencil. This allows to get a global solution to the inverse problem for the wave equation.
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 1517713
zbMATH Keywords: ordinary differential operator
zbMATH Keywords: operator pencil
zbMATH Keywords: inverse problem
zbMATH Keywords: Weyl function
zbMATH Keywords: spectral analysis
author: V. A. Yurko
reviewed by: Narcisa Apreutesei
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1517713