Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator

散射理论中最重要的问题之一是散射矩阵的刻画。本文研究了自伴算子A的奇异一阶扰动的正反向散射问题，得到了函数是A的一阶奇异扰动相移的充要条件。这一结果与点相互作用理论密切相关。

One of the most important problems in the scattering theory is the characterization of the scattering matrices. This investigation studies forward and inverse scattering problems for singular rank-one perturbations of a selfadjoint operator A. I obtain necessary and sufficient conditions for a function to be the phase shift of a singular rank-one perturbation of A. This result is closely related with the theory of point interactions.