Rank One Perturbations, Approximations, and Selfadjoint Extensions

✍ Scribed by S. Albeverio; P. Kurasov

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 331 KB
• Volume: 148
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.3050

✦ Synopsis

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 : even if the element . does not belong to H &1 (A). Approximations of the rank one perturbations are constructed in the strong operator topology. It is proven that rank one H &2 perturbations can be defined uniquely for the homogeneous operators. The results are applied to a Schro dinger operator with a delta interaction in dimension 3.

1997 Academic Press are studied in the present paper. Such perturbations were considered in a series of papers [9,12,17]. It was shown that the operator A : is well defined only if the element . belongs to the space H &1 (A) from the standard scale of Banach spaces for the nonnegative operator A and only article no. FU963050