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arXiv · 1303.6893

Expansion Theorem for Sturm-Liouville problems transmission conditions

O. Sh. Mukhtarov·K. Aydemir
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Abstract

The purpose of this paper is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green's function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space $L_{2}[a, b]$. \vskip0.3cm\noindent Keywords: Boundary-value problems, transmission conditions, Resolvent operator, expansion theorem.

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BibTeXRIS

O. Sh. Mukhtarov, K. Aydemir. 2013-03-27. Expansion Theorem for Sturm-Liouville problems transmission conditions. https://arxiv.org/abs/1303.6893

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