Spectral Properties of Discrete Klein–Gordon s-Wave Equation with Quadratic Eigenparameter-Dependent Boundary Condition

Yokus, Nihal; Coskun, Nimet

doi:10.1007/s40995-018-00672-3

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…Spectral analysis of difference equations provides a lot of information about these equations. As a result, there are many studies on the spectral analysis of discrete operators generated by difference equations recently (Yokus and Coskun, 2019;Yokus and Coskun, 2020).…”

Section: Introductionmentioning

confidence: 99%

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

Mutlu

2021

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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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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Section: Introductionmentioning

confidence: 99%

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

Mutlu

2021

Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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“…He also showed that these eigenvalues and spectral singularities are of finite number with finite multiplicities under certain conditions. Later developments in this area concerned spectral analysis of the boundary value problems of the differential and discrete operators including Sturm-Liouville, Klein-Gordon, quadratic pencils of Schrödinger and Dirac-type operators within the context of determination of Jost solution and providing suffcient conditions guaranteeing the finiteness of the eigenvalues and spectral singularities [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…Note that investigation of discrete analogues of ordinary differential operators is an important research area since difference equtions are well suited to find solutions with the aid of computers and can model many contemporary problems arising in control theory, biology, and engineering [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

The spectrum of discrete Dirac operator with a general boundary condition

Coskun

Yokus

2020

Adv Differ Equ

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In this paper, we aim to investigate the spectrum of the nonselfadjoint operator L generated in the Hilbert space l 2 (N, C 2) by the discrete Dirac system y (2) n+1-y (2) n + p n y (1) n = λy (1) n ,-y (1) n + y (1) n-1 + q n y (2) n = λy (2) n , n ∈ N, and the general boundary condition ∞ n=0 h n y n = 0, where λ is a spectral parameter, is the forward difference operator, (h n) is a complex vector sequence such that h n = (h (1) n , h (2) n), where h (i) n ∈ l 1 (N) ∩ l 2 (N), i = 1, 2, and h (1) 0 = 0. Upon determining the sets of eigenvalues and spectral singularities of L, we prove that, under certain conditions, L has a finite number of eigenvalues and spectral singularities with finite multiplicity.

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Spectral Properties of Discrete Klein–Gordon s-Wave Equation with Quadratic Eigenparameter-Dependent Boundary Condition

Cited by 2 publications

References 12 publications

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

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

The spectrum of discrete Dirac operator with a general boundary condition

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