Completeness of eigenfunctions of discontinuous Sturm-Liouville problems

E. Sen; O. Sh Mukhtarov; K. Orucoglu

doi:10.1007/s40995-016-0003-1

Completeness of eigenfunctions of discontinuous Sturm-Liouville problems

E. Sen^*, O. Sh Mukhtarov, K. Orucoglu

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 L₂[-1, 1] ⊕ C and suitable self-adjoint linear operator in it.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	Iranian Journal of Science and Technology, Transaction A: Science
Volume	40
Issue number	1
DOIs	https://doi.org/10.1007/s40995-016-0003-1
Publication status	Published - Mar 2016

Bibliographical note

Publisher Copyright:
© Shiraz University 2016.

Keywords

Eigenfunction
Eigenvalue
Resolvent operator
Sturm-liouville problem
Transmission conditions

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10.1007/s40995-016-0003-1

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title = "Completeness of eigenfunctions of discontinuous Sturm-Liouville problems",

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 L2[-1, 1] ⊕ C and suitable self-adjoint linear operator in it.",

keywords = "Eigenfunction, Eigenvalue, Resolvent operator, Sturm-liouville problem, Transmission conditions",

author = "E. Sen and Mukhtarov, \{O. Sh\} and K. Orucoglu",

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AU - Mukhtarov, O. Sh

AU - Orucoglu, K.

N1 - Publisher Copyright: © Shiraz University 2016.

PY - 2016/3

Y1 - 2016/3

N2 - 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 L2[-1, 1] ⊕ C and suitable self-adjoint linear operator in it.

AB - 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 L2[-1, 1] ⊕ C and suitable self-adjoint linear operator in it.

KW - Eigenfunction

KW - Eigenvalue

KW - Resolvent operator

KW - Sturm-liouville problem

KW - Transmission conditions

UR - https://www.scopus.com/pages/publications/84971393401

U2 - 10.1007/s40995-016-0003-1

DO - 10.1007/s40995-016-0003-1

M3 - Article

AN - SCOPUS:84971393401

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JO - Iranian Journal of Science and Technology, Transaction A: Science

JF - Iranian Journal of Science and Technology, Transaction A: Science

IS - 1

ER -

Completeness of eigenfunctions of discontinuous Sturm-Liouville problems

Abstract

Bibliographical note

Keywords

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