Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient

Mutlu, Gökhan; Arpat, Esra Kir

doi:10.16984/saufenbilder.627496

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…The utility stemmed from the interconnection of studies on direct and inverse problems with the methods of solving many problems in mathematical analysis, keeps this research area vigorous [3][4][5][6][7]. This productive and efficient subject area, originated by the pioneer work of Naimark dealing with the singular non-self-adjoint problem for ρ(x) = 1, finds itself specialized sub-areas governing different but connected techniques, for example, cases considering positive weight [8][9][10][11][12][13], non-continuous weight [14][15][16][17], sign-changing weight [18][19][20] as well as discrete cases [21][22][23][24][25][26][27][28]. Especially, the spectral singularities of the non-selfadjoint problem under the integral boundary condition has been investigated in [9,10].…”

Section: Introductionmentioning

confidence: 99%

On the Spectrum of the Non-Selfadjoint Differential Operator with an Integral Boundary Condition and Negative Weight Function

Coskun

Görgülü

2023

Universal Journal of Mathematics and Applications

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In this paper, we shall study the spectral properties of the non-selfadjoint operator in the space $L_{\varrho }^{2}\left(\mathbb{R}_{+}\right) $ generated by the Sturm-Liouville differential equation \begin{equation*} -y^{^{\prime \prime }}+q\left( x\right) y=\omega ^{2}\varrho \left( x\right) y, \quad x \in \mathbb{R}_{+} \end{equation*} with the integral type boundary condition \begin{equation*} \int \limits_{0}^{\infty }G\left( x \right) y\left( x\right) dx+ \gamma y^{\prime }\left( 0\right) -\theta y\left( 0\right) =0 \end{equation*} and the non-standard weight function \begin{equation*} \varrho \left( x\right) =-1 \end{equation*} where $\left \vert \gamma \right \vert +\left \vert \theta \right \vert \neq 0$. There are an enormous number of papers considering the positive values of $ \varrho \left( x\right) $ for both continuous and discontinuous cases. The structure of the weight function affects the analytical properties and representations of the solutions of the equation. Differently from the classical literature, we used the hyperbolic type representations of the fundamental solutions of the equation to obtain the spectrum of the operator. Moreover, the conditions for the finiteness of the eigenvalues and spectral singularities were presented. Hence, besides generalizing the recent results, Naimark's and Pavlov's conditions were adopted for the negative weight function case.

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Section: Introductionmentioning

confidence: 99%

On the Spectrum of the Non-Selfadjoint Differential Operator with an Integral Boundary Condition and Negative Weight Function

Coskun

Görgülü

2023

Universal Journal of Mathematics and Applications

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“…Studies on Sturm-Liouville differential and difference equations with matrix or operator coefficients have grown extensively in recent years (Bairamov et al, 2017;Mutlu, 2020;Mutlu and Kir Arpat 2020a;Mutlu and Kir Arpat 2020b;Aktosun and Weder, 2020). In particular, spectral properties of Sturm-Liouville differential (Aktosun and Weder, 2020) and difference equations (Aygar and Bairamov, 2012;Bairamov et al, 2016) with hermitian matrix coefficients have been examined.…”

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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Heating rate effects for the melting transition of Pt–Ag–Au nanoalloys

Yıldırım¹,

Garip²

2021

Chinese Phys. B

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The classical molecular dynamics simulations in canonical NVT ensemble conditions are used to investigate the melting transition in different heating rates of Pt-Ag-Au ternary nanoalloys. In order to obtain the initial configurations used in the molecular dynamics simulations, optimizing the chemical ordering of Pt 13 Ag n Au 42−n (n = 0-42) ternary nanoalloys was performed using the Basin-Hopping algorithm which would not allow changes in the icosahedron structure. The Gupta many-body potential was used to model interatomic interactions in both molecular dynamics simulations and optimization simulations. The melting transitions of selected Pt-Ag-Au nanoalloys were explored using caloric curves and Lindemann parameters. There have been two identified types of melting mechanisms, one includes sudden jump behavior in the caloric curve and the other is an isomerization while melting transition. The temperature range in which the isomerization takes place depends on the heating rate value.

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Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient

Cited by 4 publications

References 24 publications

On the Spectrum of the Non-Selfadjoint Differential Operator with an Integral Boundary Condition and Negative Weight Function

On the Spectrum of the Non-Selfadjoint Differential Operator with an Integral Boundary Condition and Negative Weight Function

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

Heating rate effects for the melting transition of Pt–Ag–Au nanoalloys

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