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Completeness of eigenfunctions of discontinuous Sturm–Liouville problems

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Abstract

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 \( L_{2} [ - 1,1] \oplus C \) and suitable self-adjoint linear operator in it.

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Acknowledgments

The authors are grateful for the valuable comments and suggestions of the referees.

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Authors and Affiliations

  1. Department of Mathematics Engineering, Istanbul Technical University, 34469, Maslak, İstanbul, Turkey

    E. Sen & K. Orucoglu

  2. Department of Mathematics, Gaziosmanpaşa University, 60250, Tokat, Turkey

    O. Sh. Mukhtarov

  3. Department of Mathematics, Namık Kemal University, 59030, Tekirdağ, Turkey

    E. Sen

Authors
  1. E. Sen
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  2. O. Sh. Mukhtarov
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  3. K. Orucoglu
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Correspondence to E. Sen.

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Sen, E., Mukhtarov, O.S. & Orucoglu, K. Completeness of eigenfunctions of discontinuous Sturm–Liouville problems. Iran. J. Sci. Technol. Trans. Sci. 40, 1–8 (2016). https://doi.org/10.1007/s40995-016-0003-1

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  • DOI: https://doi.org/10.1007/s40995-016-0003-1

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