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Journals / Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 11 Sayı: 4

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

Gökhan Mutlu(GAZİ ÜNİVERSİTESİ)0000-0002-0674-2908
Pages
3055–3062
Publication Date
2021-12-15
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

We also show that this operator has a finite number of eigenvalues with finite multiplicities under a certain condition on the operator coefficients.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact:We also show that this operator has a finite number of eigenvalues with finite multiplicities under a certain condition on the operator coefficients.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Discrete operator · eigenvalues · selfadjoint operators

Abstract

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.

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Cite This Article

Mutlu, G. (2021). Spectrum of Discrete Sturm-Liouville Equation with Self-adjoint Operator Coefficients on the Half-line. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 11 Sayı: 4, 3055–3062. https://doi.org/10.21597/jist.907355

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