×

A completeness theorem relative to one-dimensional Schrödinger equations with energy-dependent potentials. (English) Zbl 0545.34017

In this paper the one-dimensional Schrödinger equations with energy dependent potentials are considered as matrix eigenvalue equations. The objective of this article is the study of the corresponding inverse problems, of much interest in many diverse fields such as the theory of solitons. A completeness theorem is proven in the paper, in the sense that functions in a certain class E can be uniquely expanded through the eigenfunctions of the matrix and its adjoint.
Reviewer: J.E.Rubio

MSC:

34L99 Ordinary differential operators
PDF BibTeX XML Cite
Full Text: Numdam EuDML

References:

[1] M. Jaulent and C. Jean , Ann. Inst. Henri Poincaré , t. 25 , 1976 , p. 105 , 119 . Numdam | Zbl 0357.34018 · Zbl 0357.34018
[2] Z.S. Agranovich and V.A. Marchenko , The inverse problem of scattering Theory , Gordon and Breach , New York , 1963 . MR 162497 | Zbl 0117.06003 · Zbl 0117.06003
[3] M. Jaulent , J. Math. Phys. , t. 17 , 1976 , p. 1351 . MR 416260
[4] M. Jaulent and I. Miodek , Lett. Math. Phys. , t. 1 , 1976 , p. 243 . MR 433055 | Zbl 0342.35012 · Zbl 0342.35012
[5] C. Jean , Cahiers Mathématiques de Montpellier , n^\circ 24 , 1982 .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.