Geodesic
Reconstruction of potential and boundary conditions for second order difference equations
Commentationes Mathematicae, Tome 58 (2018) no. 1-2, p. 1–9.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, \emph{Quaestiones Mathematicae}, 40 (2017), no. 7, 861−877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
DOI : 10.14708/cm.v58i1-2.5133
Classification : 39A05, 34A55, 34K10, 65Q10, 65Q30
Mots-clés : Difference equations, inverse problem, boundary value problems, potential, eigenvalues 
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Sonja Currie; Anne Love. Reconstruction of potential and boundary conditions for second order difference equations. Commentationes Mathematicae, Tome 58 (2018) no. 1-2, p.  1–9. doi : 10.14708/cm.v58i1-2.5133. http://geodesic.mathdoc.fr/articles/10.14708/cm.v58i1-2.5133/

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