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dc.contributor.authorEsteban, Maria J.*
dc.contributor.authorLewin, Mathieu*
dc.contributor.authorSéré, Eric*
dc.date.accessioned2020-04-03T10:31:09Z
dc.date.available2020-04-03T10:31:09Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20608
dc.language.isoenen
dc.subjectDirac-Coulomb operatorsen
dc.subject.ddc520en
dc.titleDirac-Coulomb operators with general charge distribution. I. Distinguished extension and min-max formulasen
dc.typeDocument de travail / Working paper
dc.description.abstractenThis paper is the first of a series where we study the spectral properties of Dirac operators with the Coulomb potential generated by any finite signed charge distribution μ. We show here that the operator has a unique distinguished self-adjoint extension under the sole condition that μ has no atom of weight larger than or equal to one. Then we discuss the case of a positive measure and characterize the domain using a quadratic form associated with the upper spinor, following earlier works by Esteban and Loss. This allows us to provide min-max formulas for the eigenvalues in the gap. In the event that some eigenvalues have dived into the negative continuum, the min-max formulas remain valid for the remaining ones. At the end of the paper we also discuss the case of multi-center Dirac-Coulomb operators corresponding to μ being a finite sum of deltas.en
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphineen
dc.publisher.cityParisen
dc.identifier.citationpages33en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02503460en
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.identifier.citationdate2020-03
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.date.updated2020-04-03T10:28:03Z
hal.person.labIds60*
hal.person.labIds60*
hal.person.labIds60*


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