Spectrum of Discrete Sturm-Liouville Equation with Selfadjoint Operator Coefficients on the Half-line

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Atıf İçin Kopyala

Mutlu G.

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.11, sa.4, ss.3055-3062, 2021 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 11 Sayı: 4
• Basım Tarihi: 2021
• Dergi Adı: Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi
• Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.3055-3062
• Gazi Üniversitesi Adresli: Evet

Özet

We investigate the spectrum of the Sturm-Liouville difference equation on the half-line with self-adjoint operator coefficients in an infinite dimensional Hilbert space together with the Dirichlet boundary condition. We find the Jost solution and examine its analytical and asymptotical properties. Using these properties, we obtain the continuous and point spectrum of the discrete operator generated by the Sturm-Liouville difference equation with self-adjoint operator coefficients. We also show that this operator has a finite number of eigenvalues with finite multiplicities under a certain condition on the operator coefficients.