We start to discuss some aspects of the scattering theory for the Sturm–Liouville operator \(L:\dfrac{1}{y}\left[ -D^2+q\right] \). In particular, we pose and solve the problem of reconstructing the function q when y is fixed and when a set \({\mathcal {S}}\) of scattering data is given. In the meanwhile, several relations concerning the spectral properties of L and the solutions of the related eigenvalue equation are established.

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关于Sturm–Liouville算子的散射理论的一些评论

我们开始讨论Sturm–Liouville算子\（L：\ dfrac {1} {y} \ left [-D ^ 2 + q \ right] \）的散射理论的某些方面。尤其是，当y固定且给出散射数据的集合\（{\ mathcal {S}}} \）时，我们提出并解决重构函数q的问题。同时，建立了关于L的光谱性质和相关特征值方程解的几种关系。