Jost solution and the spectral properties of the matrix-valued difference operators
APPLIED MATHEMATICS AND COMPUTATION, cilt.218, sa.19, ss.9676-9681, 2012 (SCI-Expanded, Scopus)
- 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.