Fordyce A. Davidson, Bryan P. Rynne
In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form
on an arbitrary, bounded time-scale , for suitable functions , together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the Hilbert space , 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.
Submitted June 6, 2007. Published December 12, 2007.
Math Subject Classifications: 34B05, 34L05, 39A05.
Key Words: Time-scales; boundary-value problem; self-adjoint linear operators; Sobolev spaces.
Show me the PDF file (230 KB), TEX file, and other files for this article.
| Fordyce A. Davidson |
Division of Mathematics, University of Dundee
Dundee, DD1 4HN, Scotland
| Bryan P. Rynne |
Department of Mathematics and
the Maxwell Institute for Mathematical Sciences
Heriot-Watt University, Edinburgh EH14 4AS, Scotland
Return to the EJDE web page