Rank-one perturbations A(x) = A + alpha(phi,.)phi of a semibounded selfadjoint operator A are studied with the help of distribution theory. It is shown that such perturbations can be defined for finite values of alpha even if the element lp does not belong to H-1(A). Approximations of the rank one per turbations art: constructed in the strong operator topology, It is proven that rank one H-2, perturbations can he defined uniquely for the homogeneous operators. The results are applied to a Schrodinger operator with a delta interaction in dimension 3. (C) 1997 Academic Press. [References: 18]
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机译：借助分布理论研究了半界自伴算子A的秩一扰动A（x）= A + alpha（phi，.phi）。结果表明，即使元素lp不属于H-1（A），也可以为alpha的有限值定义这种扰动。每个扰动技术的秩近似：在强算子拓扑中构造，证明了H-2扰动可以为齐次算子唯一定义。将结果应用于在维度3中具有增量交互作用的Schrodinger运算符。（C）1997 Academic Press。 [参考：18]
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