Electron. J. Differential Equations, Vol. 2017 (2017), No. 136, pp. 1-17.

Spectral analysis of q-fractional Sturm-Liouville operators

Bilender P. Allahverdiev, Huseyin Tuna

In this article, we study q-fractional Sturm-Liouville operators. Using by the functional method, we pass to a new operator. Then, showing that this operator is a maximal operator and constructing a self-adjoint dilation of the maximal dissipative operator. We prove a theorem on the completeness of the system of eigenvectors and associated vectors of the dissipative q-fractional Sturm-Liouville operators.

Submitted April 4, 2017. Published May 18, 2017.
Math Subject Classifications: 47A20, 47A40, 47A45, 34B05, 34B10, 34L10, 47E05.
Key Words: Dissipative q-fractional Sturm-Liouville operator; dilation; eigenvector; scattering matrix; functional model; characteristic function.

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Bilender P. Allahverdiev
Department of Mathematics
Faculty of Arts and Sciences
Süleyman Demirel University
32260 Isparta, Turkey
email: bilenderpasaoglu@sdu.edu.tr
Hüseyin Tuna
Department of Mathematics
Faculty of Arts and Sciences
Mehmet Akif Ersoy University
15030 Burdur, Turkey
email: hustuna@gmail.com

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