Spectral analysis of a selfadjoint matrix-valued discrete operator on the whole axis

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BAYRAM E., AYGAR KÜÇÜKEVCİLİOĞLU Y., Cebesoy S.

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, cilt.9, sa.6, ss.4257-4262, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 6
  • Basım Tarihi: 2016
  • Doi Numarası: 10.22436/jnsa.009.06.67
  • Dergi Adı: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4257-4262
  • Anahtar Kelimeler: Difference equations, discrete operator, Jost solution, eigenvalue, continuous spectrum, DIFFERENCE-OPERATORS, SINGULARITIES
  • Ankara Üniversitesi Adresli: Evet

Özet

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. (C) 2016 All rights reserved.