Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis
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Authors
Elgiz Bairamov
- Faculty of Science, Department of Mathematics, University of Ankara, 06100, Ankara, Turkey.
Yelda Aygar
- Faculty of Science, Department of Mathematics, University of Ankara, 06100, Ankara, Turkey.
Serifenur Cebesoy
- Faculty of Science, Department of Mathematics, University of Ankara, 06100, Ankara, Turkey.
Abstract
The spectral analysis of matrix-valued difference equations of second order having polynomial-type Jost
solutions, was first used by Aygar and Bairamov. They investigated this problem on semi-axis. The main aim
of this paper is to extend similar results to the whole axis. We find polynomial-type Jost solutions of a second
order matrix selfadjoint difference equation to the whole axis. Then, we obtain the analytical properties
and asymptotic behaviors of these Jost solutions. Furthermore, we investigate continuous spectrum and
eigenvalues of the operator \(L\) generated by a matrix-valued difference expression of second order. Finally,
we get that the operator \(L\) has a finite number of real eigenvalues.
Share and Cite
ISRP Style
Elgiz Bairamov, Yelda Aygar, Serifenur Cebesoy, Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4257--4262
AMA Style
Bairamov Elgiz, Aygar Yelda, Cebesoy Serifenur, Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis. J. Nonlinear Sci. Appl. (2016); 9(6):4257--4262
Chicago/Turabian Style
Bairamov, Elgiz, Aygar, Yelda, Cebesoy, Serifenur. "Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4257--4262
Keywords
- Difference equations
- discrete operator
- Jost solution
- eigenvalue
- continuous spectrum.
MSC
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