Essential spectrum and L(2)-solutions of one-dimensional Schrodinger operators

DC FieldValueLanguage
dc.contributor.authorRemling, C
dc.date.accessioned2021-12-23T16:01:27Z-
dc.date.available2021-12-23T16:01:27Z-
dc.date.issued1996
dc.identifier.issn00029939
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/4971-
dc.description.abstractIn 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrodinger operator possess square integrable solutions, then the essential spectrum is' nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrodinger operators which satisfy the condition of existence of L(2)-solutions. The proof of this theorem is based on inverse spectral theory.
dc.language.isoen
dc.publisherAMER MATHEMATICAL SOC
dc.relation.ispartofPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
dc.subjectessential spectrum
dc.subjectHartman-Wintner conjecture
dc.subjectinverse spectral theory
dc.subjectL(2)-solution
dc.subjectMathematics
dc.subjectMathematics, Applied
dc.subjectone-dimensional Schrodinger operator
dc.titleEssential spectrum and L(2)-solutions of one-dimensional Schrodinger operators
dc.typejournal article
dc.identifier.doi10.1090/S0002-9939-96-03463-6
dc.identifier.isiISI:A1996UX87800019
dc.description.volume124
dc.description.issue7
dc.description.startpage2097
dc.description.endpage2100
dc.publisher.place201 CHARLES ST, PROVIDENCE, RI 02940-2213
dcterms.isPartOf.abbreviationProc. Amer. Math. Soc.
dcterms.oaStatusBronze
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