On the determination of self-adjoint differential operators on the semiaxis
type: Item
instance of: scholarly article
title: On the determination of self-adjoint differential operators on the semiaxis
zbMATH Open document ID: 0839.34018
DOI: 10.1007/BF02303979
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: The author studies the inverse problem of recording the differential operators \((\ell, U_\xi)\) in the equations \[ ly = y^{(n)} + \sum^{n - 2}_{\nu = 0} p_\nu (x)y^{(\nu)} = \lambda y, \quad x > 0,\;p_\nu(x) \in {\mathcal L} (0, \infty), \] \[ U_\xi (y) = y^{(\sigma_\xi)} (0) + \sum^{\sigma_\xi - 1}_{\nu = 0} u_{\xi \nu} y^{(\nu)} (0), \quad \xi = 1, \dots, n,\;0 \leq \sigma_\xi \leq n - 1 \] from the Weil solutions \(\Phi_1 (x, \lambda), \dots, \Phi_n (x, \lambda)\) and the corresponding Weil matrix \({\mathfrak M} (\lambda)\) with entries \(U_{km} (\lambda) = U_m (\Phi_k)\). The techniques use previous results of the author published in [Mat. Sb. 182, No. 3, 431-456 (1991; Zbl 0782.34021)].
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 846505
zbMATH Keywords: inverse problem
zbMATH Keywords: Weil solutions
author: V. A. Yurko
reviewed by: Jürgen Appell
MaRDI profile type: Publication
cites work: Q3360509
cites work: Q3480393
cites work: Q3252800
cites work: The Inverse Problem for Ordinary Differential Operators on the Line
cites work: Q3807556
cites work: Q3994426
cites work: Solution of the Boussinesq equation on the half-line by the inverse problem method
cites work: Q5624013
cites work: Q3697388
full work available at URL: https://doi.org/10.1007/bf02303979
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description: scientific article; zbMATH DE number 846505