Singular rank one perturbations

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dc.contributor.authorAstaburuaga, M. A.
dc.contributor.authorCortes, V. H.
dc.contributor.authorFernandez, C.
dc.contributor.authorDel Rio, R.
dc.date.accessioned2025-01-20T22:00:29Z
dc.date.available2025-01-20T22:00:29Z
dc.date.issued2022
dc.description.abstractIn this paper, A = B + V represents a self-adjoint operator acting on a Hilbert space H. We set a general theoretical framework and obtain several results for singular perturbations of A of the type A(beta) = A + beta tau*tau for tau being a functional defined in a subspace of H. In particular, we apply these results to H-beta = -Delta + V + beta|delta ><delta|, where delta is the singular perturbation given by delta(phi) = integral(S)phi d sigma, where S is a suitable hypersurface in R-n. Using the fact that the singular perturbation tau*tau is a sort of rank one perturbation of the operator A, it is possible to prove the invariance of the essential spectrum of A under these singular perturbations. The main idea is to apply an adequate Krein's formula in this singular framework. As an additional result, we found the corresponding relationship between the Green's functions associated with the operators H-0 = Delta + V and H-beta, and we give a result about the existence of a pure point spectrum (eigenvalues) of H-beta. We also study the case beta goes to infinity.
dc.fuente.origenWOS
dc.identifier.doi10.1063/5.0061250
dc.identifier.eissn1089-7658
dc.identifier.issn0022-2488
dc.identifier.urihttps://doi.org/10.1063/5.0061250
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/93724
dc.identifier.wosidWOS:000752321600001
dc.issue.numero2
dc.language.isoen
dc.revistaJournal of mathematical physics
dc.rightsacceso restringido
dc.titleSingular rank one perturbations
dc.typeartículo
dc.volumen63
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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