| 1. |
- Albeverio, S., et al.
(författare)
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Finite rank perturbations and distribution theory
- 1999
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Ingår i: Proceedings of the American Mathematical Society. - 0002-9939 .- 1088-6826. ; 127:4, s. 1151-1161
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Tidskriftsartikel (refereegranskat)abstract
- Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2A) to H-2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.
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| 2. |
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| 3. |
- Albeverio, S., et al.
(författare)
-
Rank one perturbations of not semibounded operators
- 1997
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Ingår i: Integral equations and operator theory. - 0378-620X .- 1420-8989. ; 27:4, s. 379-400
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Tidskriftsartikel (refereegranskat)abstract
- 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
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| 4. |
- Albeverio, S., et al.
(författare)
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S-matrix, resonances, and wave functions for transport through billiards with leads
- 1996
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 37:10, s. 4888-4903
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Tidskriftsartikel (refereegranskat)abstract
- For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator
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| 5. |
- Albeverio, S., et al.
(författare)
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Symmetries of Schrödinger operator with point interactions
- 1998
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Ingår i: Letters in Mathematical Physics. - 0377-9017 .- 1573-0530. ; 45, s. 33-47
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Tidskriftsartikel (refereegranskat)abstract
- The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon
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