Bilender P. Allahverdiev, Aytekin Eryilmaz, Huseyin Tuna
Abstract:
In this article we consider a second-order Sturm-Liouville operator with a
spectral parameter in the boundary condition on bounded time scales.
We construct a selfadjoint dilation of the dissipative Sturm-Liouville
operators. Using by methods of Pavlov [40,41,42], we prove the completeness
of the system of eigenvectors and associated vectors of the
dissipative Sturm-Liouville operators on bounded time scales.
Submitted February 29, 2016. Published April 5, 2017.
Math Subject Classifications: 47A20, 47A40, 47A45, 34B05, 34B10, 39A10.
Key Words: Time scale; delta-differentiable; dilation; dissipative operator;
system of eigenvectors; scattering matrix; functional model;
characteristic function.
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Bilender P. Allahverdiev Department of Mathematics Faculty of Arts and Science Süleyman Demirel University 32260 Isparta, Turkey email: bilenderpasaoglu@sdu.edu.tr |
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Aytekin Eryilmaz Department of Mathematics Nevsehir University Nevsehir, Turkey email: eryilmazaytekin@gmail.com |
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Hüseyin Tuna Department of Mathematics Mehmet Akif Ersoy University Burdur, Turkey email: hustuna@gmail.com |
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