Rank one perturbations of not semibounded operators

Godkänd; 1997; 20090207 (andbra)
Rank one perturbations of selfadjoint operators which are not necessarily semibounded are studied in the present paper. It is proven that such perturbations are uniquely defined, if they are bounded in the sense of forms. We also show that form unbounded rank one perturbations can be uniquely defined if the original operator and the perturbation are homogeneous with respect to a certain one parameter semigroup. The perturbed operator is defined using the extension theory for symmetric operators. The resolvent of the perturbed operator is calculated using Krein's formula. It is proven that every rank one perturbation can be approximated in the operator norm. We prove that some form unbounded perturbations can be approximated in the strong resolvent sense without renormalization of the coupling constant only if the original operator is not semibounded. The present approach is applied to study first derivative and Dirac operators with point interaction, in one dimension

Kurasov, PavelLund University,Lunds universitet,Stockholms universitet,Luleå tekniska universitet,Analysis,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH(Swepub:lu)math-pko (författare)
Luleå tekniska universitetDepartment of Mathematics, Ruhr-University, Bochum (creator_code:org_t)

Ingår i:Integral equations and operator theory27:4, s. 379-4000378-620X1420-8989

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Av lärosätet: Luleå tekniska universitet; Stockholms universitet; Lunds universitet

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