On approximations of rank one ℋ₋₂-perturbations

Albeverio, S.; Koshmanenko, V.; Kurasov, P.; Nizhnik, L.

doi:10.1090/S0002-9939-02-06694-7

On approximations of rank one ${\mathcal H}_{-2}$-perturbations
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by S. Albeverio, V. Koshmanenko, P. Kurasov and L. Nizhnik PDF

Proc. Amer. Math. Soc. 131 (2003), 1443-1452 Request permission

Abstract:

Approximations of rank one ${\mathcal H}_{-2}$-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.

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