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Rank one perturbati...
Rank one perturbations of not semibounded operators
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- Albeverio, S. (författare)
- Department of Mathematics, Ruhr-University, Bochum
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- Kurasov, Pavel (författare)
- Lund 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
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(creator_code:org_t)
- 1997
- 1997
- Engelska.
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Ingår i: Integral equations and operator theory. - 0378-620X .- 1420-8989. ; 27:4, s. 379-400
- Relaterad länk:
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https://urn.kb.se/re...
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visa fler...
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https://doi.org/10.1...
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https://urn.kb.se/re...
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https://lup.lub.lu.s...
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Abstract
Ämnesord
Stäng
- 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
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Mathematics
- Matematik
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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