Jost solution and the spectral properties of the matrix-valued difference operators

AYGAR KÜÇÜKEVCİLİOĞLU Y., BAYRAM E.

APPLIED MATHEMATICS AND COMPUTATION, cilt.218, sa.19, ss.9676-9681, 2012 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 218 Sayı: 19
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.amc.2012.02.081
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.9676-9681
  • Anahtar Kelimeler: Difference equations, Spectral analysis, Eigenvalues, Continuous spectrum, Jost function, SCHRODINGER OPERATOR, BOUNDARY-CONDITION, QUADRATIC PENCIL, SINGULARITIES, EQUATIONS, EXPANSION, SYSTEM
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we find polynomial type Jost solution of the selfadjoint matrix-valued difference equation of second order. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem we prove that, the selfadjoint operator L generated by the matrix-valued difference expression of second order has the continuous spectrum filling the segment [-2, 2]. We also study the eigenvalues of L and prove that it has a finite number of simple real eigenvalues. (C) 2012 Elsevier Inc. All rights reserved.