Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials

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dc.contributor.authorVougalter, V
dc.date.accessioned2021-10-08T07:08:20Z
dc.date.available2021-10-08T07:08:20Z
dc.date.issued2013
dc.description.abstractWe establish sharp semiclassical upper bounds for the moments of some negative powers for the eigenvalues of the Dirichlet Laplacian. When a constant magnetic field is incorporated in the problem, we obtain sharp lower bounds for the moments of positive powers not exceeding one for such eigenvalues. When considering a Schrödinger operator with the relativistic kinetic energy and a smooth, nonnegative, unbounded potential, we prove the sharp Lieb-Thirring estimate for the moments of some negative powers of its eigenvalues.
dc.identifier.apacitationVougalter, V. (2013). Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials. <i>Mathematical Modelling of Natural Phenomena</i>, 8(1), 237 - 245. http://hdl.handle.net/11427/34559en_ZA
dc.identifier.chicagocitationVougalter, V "Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials." <i>Mathematical Modelling of Natural Phenomena</i> 8, 1. (2013): 237 - 245. http://hdl.handle.net/11427/34559en_ZA
dc.identifier.citationVougalter, V. 2013. Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials. <i>Mathematical Modelling of Natural Phenomena.</i> 8(1):237 - 245. http://hdl.handle.net/11427/34559en_ZA
dc.identifier.issn0973-5348
dc.identifier.issn1760-6101
dc.identifier.ris TY - Journal Article AU - Vougalter, V AB - We establish sharp semiclassical upper bounds for the moments of some negative powers for the eigenvalues of the Dirichlet Laplacian. When a constant magnetic field is incorporated in the problem, we obtain sharp lower bounds for the moments of positive powers not exceeding one for such eigenvalues. When considering a Schrödinger operator with the relativistic kinetic energy and a smooth, nonnegative, unbounded potential, we prove the sharp Lieb-Thirring estimate for the moments of some negative powers of its eigenvalues. DA - 2013 DB - OpenUCT DP - University of Cape Town IS - 1 J1 - Mathematical Modelling of Natural Phenomena LK - https://open.uct.ac.za PY - 2013 SM - 0973-5348 SM - 1760-6101 T1 - Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials TI - Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials UR - http://hdl.handle.net/11427/34559 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/34559
dc.identifier.vancouvercitationVougalter V. Sharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials. Mathematical Modelling of Natural Phenomena. 2013;8(1):237 - 245. http://hdl.handle.net/11427/34559.en_ZA
dc.language.isoeng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.sourceMathematical Modelling of Natural Phenomena
dc.source.journalissue1
dc.source.journalvolume8
dc.source.pagination237 - 245
dc.source.urihttps://dx.doi.org/10.1051/mmnp/20138119
dc.subject.othersemiclassical bounds
dc.subject.otherLieb-Thirring inequalities
dc.subject.otherunbounded potentials
dc.subject.othermagnetic fields
dc.titleSharp Semiclassical Bounds for the Moments of Eigenvalues for Some Schrödinger Type Operators with Unbounded Potentials
dc.typeJournal Article
uct.type.publicationResearch
uct.type.resourceJournal Article
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