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Rank one perturbations of not semibounded operators
Department of Mathematics, Ruhr-University, Bochum.
Luleå tekniska universitet.
1997 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 27, no 4, p. 379-400Article in journal (Refereed) Published
Abstract [en]

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

Place, publisher, year, edition, pages
1997. Vol. 27, no 4, p. 379-400
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-5592DOI: 10.1007/BF01192120Local ID: 3ba0b230-f50d-11dd-a85e-000ea68e967bOAI: oai:DiVA.org:ltu-5592DiVA: diva2:978466
Note
Godkänd; 1997; 20090207 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-21Bibliographically approved

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