A note on spectral properties of a Dirac system with matrix coefficient

Volume 10, Issue 4, pp 1459--1469 http://dx.doi.org/10.22436/jnsa.010.04.15

Publication Date: April 20, 2017 Submission Date: April 24, 2016

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Authors

Yelda Aygar - Faculty of Science, Department of Mathematics, University of Ankara, 06100, Ankara, Turkey. Elgiz Bairamov - Faculty of Science, Department of Mathematics, University of Ankara, 06100, Ankara, Turkey. Seyhmus Yardimci - Faculty of Science, Department of Mathematics, University of Ankara, 06100, Ankara, Turkey.

Abstract

In this paper, we find a polynomial-type Jost solution of a self-adjoint matrix-valued discrete Dirac system. Then we investigate analytical properties and asymptotic behavior of this Jost solution. Using the Weyl compact perturbation theorem, we prove that matrix-valued discrete Dirac system has continuous spectrum filling the segment [-2, 2]. Finally, we examine the properties of the eigenvalues of this Dirac system and we prove that it has a finite number of simple real eigenvalues.

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Keywords

• Discrete Dirac system
• spectral analysis
• Jost solution
• eigenvalue.

MSC

•  39A05
•  39A70
•  39A10
•  47A05
•  47A10

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