Self-adjoint boundary-value problems on time-scales

Fordyce A. Davidson, Bryan P. Rynne

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    NOTE: THE MATHEMATICAL SYMBOLS IN THIS ABSTRACT CANNOT BE DISPLAYED CORRECTLY ON THIS PAGE. PLEASE REFER TO THE ABSTRACT IN THE ATTACHED FILE OR THE PUBLISHERS WEBSITE FOR AN ACCURATE DISPLAY. In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form Lu := -[pur] + 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(T ), 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.
    Original languageEnglish
    Pages (from-to)1-10
    Number of pages10
    JournalElectronic Journal of Differential Equations
    Issue number175
    Publication statusPublished - 2007


    • Boundary value problems


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