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On approximations of rank one |
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| Authors: | S Albeverio V Koshmanenko P Kurasov L Nizhnik |
| Institution: | Institute für Angewandte Mathematik, Univ. Bonn, Wegelerstr. 6, 53155 Bonn, Germany; SFB 256 Bonn, BiBoS, Bielefeld-Bonn, CERFIM, Locarno and USI (Switzerland) ; Institute of Mathematics, vul. Tereschenkivs'ka, 3, Kyiv, 01601 Ukraine ; Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden ; Institute of Mathematics, vul. Tereschenkivs'ka, 3, Kyiv, 01601 Ukraine |
| Abstract: | Approximations of rank one  -perturbations of self-adjoint operators by operators with regular rank one perturbations are discussed. It is proven that in the case of arbitrary not semibounded operators such approximations in the norm resolvent sense can be constructed without any renormalization of the coupling constant. Approximations of semibounded operators are constructed using rank one non-symmetric regular perturbations. |
| Keywords: | Self-adjoint operators singular interactions |
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