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dc.contributor.authorVeliev, Oktay A.
dc.date.accessioned2016-12-20T14:17:52Z
dc.date.available2016-12-20T14:17:52Z
dc.date.issued2007
dc.identifier.citationVeliev, O. A. (2007). Perturbation Theory for the Periodic Multidimensional Schrödinger Operator and the Bethe-Sommerfeld Conjecture. International Journal Of Contemporary Mathematical Sciences, 2(2), 19-87.en_US
dc.identifier.issn1312-7586
dc.identifier.issn1314-7544
dc.identifier.urihttp://hdl.handle.net/11376/2814
dc.descriptionVeliev, Oktay A. (Dogus Author)en_US
dc.description.abstractIn this paper we obtain asymptotic formulas of arbitrary order for the Bloch eigenvalue and the Bloch function of the periodic Schr¨odinger operatör −Δ + q(x), of arbitrary dimension, when corresponding quasimomentum lies near a diffraction hyperplane. Besides, writing the asymptotic formulas for the Bloch eigenvalue and the Bloch function, when corresponding quasimomentum lies far from the diffraction hyperplanes, obtained in my previous papers in improved and enlarged form, we obtain the complete perturbation theory for the multidimensional Schr¨odinger operator with a periodic potential. Moreover, we estimate the measure of the isoenergetic surfaces in the high energy region which implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimension and arbitrary lattice.en_US
dc.language.isoengen_US
dc.publisherHikarien_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectPeriodic Schrödinger Operatoren_US
dc.subjectPerturbation Theoryen_US
dc.titlePerturbation theory for the periodic multidimensional Schrödinger Operator and the Bethe-Sommerfeld Conjectureen_US
dc.typearticleen_US
dc.relation.journalInternational Journal Of Contemporary Mathematical Sciencesen_US
dc.contributor.departmentDoğuş Üniversitesi, Mühendislik Fakültesi, Makine Mühendisliği Bölümüen_US
dc.contributor.authorIDTR55504en_US
dc.identifier.volume2en_US
dc.identifier.issue2en_US
dc.identifier.startpage19en_US
dc.identifier.endpage87en_US


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