Property C for ODE and applications to inverse problems
数学物理
2007-05-23 v1 偏微分方程分析
math.MP
数值分析
摘要
Property C stands for completeness of the set of products of solutions to homogeneous linear differential equations. property C is proved in various formulations for Schr\"odinger operators. Many applications of this property to inverse problems and inverse scattering problems are given. It is shown what part of the fixed-energy phase shifts determines a compactly supported potential uniquely. It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis.
引用
@article{arxiv.math-ph/9911032,
title = {Property C for ODE and applications to inverse problems},
author = {A. G. Ramm},
journal= {arXiv preprint arXiv:math-ph/9911032},
year = {2007}
}