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


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AYGAR KÜÇÜKEVCİLİOĞLU Y., BAYRAM E., YARDIMCI Ş.

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, vol.10, no.4, pp.1459-1469, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.22436/jnsa.010.04.15
  • Journal Name: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), zbMATH
  • Page Numbers: pp.1459-1469
  • Keywords: Discrete Dirac system, spectral analysis, Jost solution, eigenvalue, OPERATORS
  • Ankara University Affiliated: Yes

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. (C) 2017 All rights reserved.