常微分方程的性质C及其在反问题中的应用
Property C for ODE and applications to inverse problems
AI总结：
本文证明了薛定谔算子的性质C（齐次线性微分方程解乘积的完备性），并将其应用于反问题和逆散射问题，揭示了固定能量相移对紧支撑势的唯一确定，并指出Newton-Sabatier方法本质上是参数拟合而非反演方法。
摘要：
性质C表示齐次线性微分方程解乘积的完备性。对于薛定谔算子，性质C在各种形式下得到证明。给出了该性质在反问题和逆散射问题中的许多应用。展示了固定能量相移的哪一部分唯一确定一个紧支撑势。证明了Newton-Sabatier方法并非真正的反演方法，而是一种参数拟合过程，并证明该过程无法恢复一般势，特别是任何在正实轴邻域内非解析的势。
英文摘要：
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 Schrödinger 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
