Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit
摘要
In present article the self-contained derivation of eigenvalue inverse problem results is given by using a discrete approximation of the Schroedinger operator on a bounded interval as a finite three-diagonal symmetric Jacobi matrix. This derivation is more correct in comparison with previous works which used only single-diagonal matrix. It is demonstrated that inverse problem procedure is nothing else than well known Gram-Schmidt orthonormalization in Euclidean space for special vectors numbered by the space coordinate index. All the results of usual inverse problem with continuous coordinate are reobtained by employing a limiting procedure, including the Goursat problem -- equation in partial derivatives for the solutions of the inversion integral equation.
引用
@article{arxiv.math-ph/0312012,
title = {Inverse eigenvalue problem for discrete three-diagonal Sturm-Liouville operator and the continuum limit},
author = {Vladimir M. Chabanov and Boris N. Zakhariev},
journal= {arXiv preprint arXiv:math-ph/0312012},
year = {2009}
}
备注
19 pages There were made some additions (and reformulations) to the text making the derivation of the results more precise and understandable