Self-adjoint boundary-value problems on time-scales
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In 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.
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.
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