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 double-struck 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 L 2(double-struck 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. ©2007 Texas State University.
|Number of pages||10|
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 12 Dec 2007|
- Boundary-value problem
- Self-adjoint linear operators
- Sobolev spaces