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Completeness of eigenfunctions of discontinuous Sturm-Liouville problems
(Springer International Publishing Ag, 2016) Şen, Erdoğan; Mukhtarov, O.; Oruçoğlu, Kamil
In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm-Liouville problem with discontinuities at two points. The problem contains an eigenparameter in one of the boundary conditions. For operator-theoretic formulation of the considered problem we define an equivalent inner product in the Hilbert space L-2[-1, 1] circle plus C and suitable self-adjoint linear operator in it.
Spectral Properties of Discontinuous Sturm-Liouville Problems with a Finite Number of Transmission Conditions
(Springer Basel Ag, 2016) Şen, Erdoğan; Mukhtarov, O.
In this paper we investigate discontinuous two-point boundary value problems with eigenparameter in the boundary conditions and with transmission conditions at the finitely many points of discontinuity. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of the considered problem coincide with those of A. We obtain asymptotic formulas for the eigenvalues and eigenfunctions. Also we show that the eigenelements of A are complete in H.