On The Solution of an Infinite System of Discrete Equations
Turkish Journal of Mathematics and Computer Science, cilt.12, sa.2, ss.157-160, 2020 (Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 12 Sayı: 2
- Basım Tarihi: 2020
- Doi Numarası: 10.47000/tjmcs.822830
- Dergi Adı: Turkish Journal of Mathematics and Computer Science
- Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.157-160
- Anahtar Kelimeler: Difference equation, Direct problem, Inverse problem, Jacobi matrix, Transformation operators
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
In this work, we construct the transformation operator for the infinite system of the difference equations an−2yn−2 + bn−1yn−1 + cnyn + bnyn+1 + anyn+2 = λyn (n = 1, 2, …), where an ≠ 0, bn, cn (n = 1, 2, 3, …) are given complex numbers, investigate some important properties of the special solutions of the difference system. symmetric matrices. But in these studies the special Fourier type series representations of the solutions of an even order difference system was not considered and logically the direct and inverse scattering problems for the (2N + 1)-diagonal Jacobi matrices as generalization of G.Sh. Guseinov’s result have not yet investigated. In this work, as the first step of the investigation the direct and inverse scattering problems for the five-diagonal Jacobi matrices by the Marchenko method, we construct the transformation operator for the infinite system of the difference equations.