For a given self-adjoint operator A with discrete spectrum, we completely characterise possible eigenvalues of its rank-one perturbations B and discuss the inverse problem of reconstructing B from its spectrum.

中文翻译：

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自伴算子的一阶摄动的正谱和反谱问题

对于给定的具有离散频谱的自伴算子A，我们完全刻画了其秩一扰动B的可能特征值， 并讨论了从其频谱重构B的反问题。