Self-adjoint boundary-value problems on time-scales

Date

2007-12-12

Authors

Davidson, Fordyce A.
Rynne, Bryan

Journal Title

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Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

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.

Description

Keywords

Time-scales, Boundary-value problem, Self-adjoint linear operators, Sobolev spaces

Citation

Davidson, F. A., & Rynne, B. P. (2007). Self-adjoint boundary-value problems on time-scales. <i>Electronic Journal of Differential Equations, 2007</i>(175), pp. 1-10.

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Attribution 4.0 International

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