Self-adjoint boundary-value problems on time-scales

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dc.contributor.authorDavidson, Fordyce A.
dc.contributor.authorRynne, Bryan
dc.date.accessioned2021-08-19T17:28:04Z
dc.date.available2021-08-19T17:28:04Z
dc.date.issued2007-12-12
dc.description.abstractIn this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := -[pu∇]∆ + qu, on an arbitrary, bounded time-scale T, for suitable functions p, q, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space L2(Tk), in such a way that the resulting operator is self-adjoint, with compact resolvent (here, 'self-adjoint' means in the standard functional analytic meaning of this term). Previous discussions of operators of this, and similar, form have described them as 'self-adjoint', but have not demonstrated self-adjointness in the standard functional analytic sense.
dc.description.departmentMathematics
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDavidson, F. A., & Rynne, B. P. (2007). Self-adjoint boundary-value problems on time-scales. Electronic Journal of Differential Equations, 2007(175), pp. 1-10.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14394
dc.language.isoen
dc.publisherTexas State University-San Marcos, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectTime-scales
dc.subjectBoundary-value problem
dc.subjectSelf-adjoint linear operators
dc.subjectSobolev spaces
dc.titleSelf-adjoint boundary-value problems on time-scales
dc.typeArticle

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