Monodromy matrix for linear difference operators with almost constant coefficients
type: Item
instance of: scholarly article
title: Monodromy matrix for linear difference operators with almost constant coefficients
zbMATH Open document ID: 0843.39014
author: Aurelija Trgo
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-05-13T00:00:00Z
review text: A new method for solving the direct scattering problem associated with a linear difference operator of arbitrary order \[ L = \widetilde p_{-k} (t) E^{-k} + \widetilde p_{- k + 1} (t) E^{- k + 1} + \cdots + \widetilde p_{m - 1} (t) E^{m - 1} + \widetilde p_m (t) E^m, \] is presented. A procedure for analysing the behavior of the monodromy operator (monodromy matrix) under the influence of shift is also presented. Finally it is proved that the second-order self adjoint difference operator (corresponding to the discrete Schrödinger scattering problem) associated with the Toda lattice equations possesses the \(l^2\)-eigenfunctions.
Mathematics Subject Classification ID: 39A70
zbMATH DE Number: 859229
zbMATH Keywords: eigenfunctions
zbMATH Keywords: monodromy matrix
zbMATH Keywords: direct scattering problem
zbMATH Keywords: linear difference operator
zbMATH Keywords: second-order self adjoint difference operator
zbMATH Keywords: discrete Schrödinger scattering problem
zbMATH Keywords: Toda lattice
reviewed by: B. M. Agrawal
MaRDI profile type: Publication
OpenAlex ID: W2031298142
DOI: 10.1006/JMAA.1995.1324
description: scientific article; zbMATH DE number 859229