ODE和应用的特性C
Property C for ODE and applications
摘要：
作者的结果的概述。定义了常微分方程的C性质，证明了Sturm-Liouville算子对具有C性质.这一性质适用于许多反问题。利用性质C，用一种新的简洁方法证明了一些著名的结果，如从散射数据、从谱函数和从两个谱恢复势的唯一性。得到了许多新的结果。特别是，它被证明是一个compensated支持的潜力可以唯一地恢复从相移的s波单独，已知在所有的能量，没有知识的束缚态和赋范常数。已知在某些角动量值处的固定能量相移唯一地确定了一个紧支势。研究了混合数据反问题。分析了Newton-Sabatier过程。它表明，这个过程是一个参数拟合过程，而不是一个反演方法。反问题的其他结果。
英文摘要：
An overview of the authors results is given. Property C for ODE is defioned, It is proved that the pair of Sturm-Liouville operators has property C. This property is applied to many inverse problems. Some well-known results, such as uniqueness of the recovery of the potential from scattering data, from the spectral function and from two spectra are proved in a new short way based on property C. Many new results are obtained. In particular, it is proved that a compactly supported potential can be uniquely recovered from the phase shift of s-wave alone, known at all energies, without knowledge of bound states and norming constants. The fixed-energy phase shifts known at some values of the angular momentum determine a compactly supported potential uniquely. Mixed data inverse problems are studied. Analysis of the Newton-Sabatier procedure is given. It is shown that this procedure is a parameter-fitting procedure rather than an inversion method. Other results on inverse problems are obtained.
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