Deficiency indices and spectral theory of third order differential operators on the half line

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dc.contributor.authorBehncke, H
dc.contributor.authorHinton, D
dc.date.accessioned2021-12-23T16:13:42Z-
dc.date.available2021-12-23T16:13:42Z-
dc.date.issued2005
dc.identifier.issn0025584X
dc.identifier.urihttps://osnascholar.ub.uni-osnabrueck.de/handle/unios/10702-
dc.description.abstractWe investigate the spectral theory of a general third order formally symmetric differential expression of the form L[y] = 1/w {-i(q(0)(q(0)y')')' i (q(1)y' (q(1)y)') - (p(0)y')' p(1)y} acting in the Hilbert space L-w(2) (a, infinity). A Kummer-Liouville transformation is introduced which produces a differential operator unitarily equivalent to L. By means of the Kummer-Liouville transformation and asymptotic integration, the asymptotic solutions of L[y] = zy are found. From the asymptotic integration, the deficiency indices are found for the minimal operator associated with L. For a class of operators with deficiency index (2, 2), it is further proved that almost all selfadjoint extensions of the minimal operator have a discrete spectrum which is necessarily unbounded below. There are however also operators with continuous spectrum. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
dc.language.isoen
dc.publisherWILEY-V C H VERLAG GMBH
dc.relation.ispartofMATHEMATISCHE NACHRICHTEN
dc.subjectASYMPTOTIC INTEGRATION
dc.subjectasymptotic solutions
dc.subjectdeficiency indices
dc.subjectEQUATIONS
dc.subjectMathematics
dc.subjectspectral theory
dc.titleDeficiency indices and spectral theory of third order differential operators on the half line
dc.typejournal article
dc.identifier.doi10.1002/mana.200310314
dc.identifier.isiISI:000232599200004
dc.description.volume278
dc.description.issue12-13
dc.description.startpage1430
dc.description.endpage1457
dc.identifier.eissn15222616
dc.publisher.placePOSTFACH 101161, 69451 WEINHEIM, GERMANY
dcterms.isPartOf.abbreviationMath. Nachr.
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