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

Creative Commons License

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

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, cilt.10, sa.4, ss.1459-1469, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 4
  • Basım Tarihi: 2017
  • Doi Numarası: 10.22436/jnsa.010.04.15
  • Dergi Adı: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), zbMATH
  • Sayfa Sayıları: ss.1459-1469
  • Anahtar Kelimeler: Discrete Dirac system, spectral analysis, Jost solution, eigenvalue, OPERATORS
  • Ankara Üniversitesi Adresli: Evet

Özet

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.