Inverse spectral problem for non-selfadjoint Dirac operator with boundary and jump conditions dependent on the spectral parameter

Wei, Zengxin; Wei, Guangsheng

doi:10.1016/j.cam.2016.05.018

Cited by 12 publications

(3 citation statements)

References 17 publications

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“…In 2016, Wei et al investigated the inverse spectral problem for Dirac operator with boundary and jump conditions dependent on the spectral parameter. Through inducting the generalized normal constants they have proved the uniqueness theorem, then a construction method for solving this inverse problem was given [30]. In 2018 and 2021, Bartels et al presented Sturm-Liouville problems with transfer condition Herglotz dependent on the eigenparameter, and showed the Hilbert space formulation of the problem and calculated out the eigenvalue and eigenfunction asymptotic formula on this problem [31] [34].…”

Section: Introductionmentioning

confidence: 99%

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

Zhao,

2024

JAMP

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In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.

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Section: Introductionmentioning

confidence: 99%

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

Zhao,

2024

JAMP

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“…Direct and inverse problems for continuous Sturm-Liouville equations with eigenparameter dependent boundary conditions have been studied extensively (see [4,5,10,14,16] for a sample of the literature). Investigations into Sturm-Liouville equations with discontinuity conditions depending on the spectral parameter have been thus far limited to the affine case (see [2,12,17,19]) and affine dependence of the square root of the eigenparameter, see [13]. In particular, transmission conditions of the form…”

Section: Introductionmentioning

confidence: 99%

“…where c ∈ R + and h is affine in λ were considered in [19], and c = 1 and h(λ) = iα √ λ, α > 0 in [13]. Recently, the discontinuity condition…”

Section: Introductionmentioning

confidence: 99%

Sturm–Liouville Problems with Transfer Condition Herglotz Dependent on the Eigenparameter: Hilbert Space Formulation

Bartels

Currie

Nowaczyk

et al. 2018

Integr. Equ. Oper. Theory

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We consider a Sturm-Liouville equation ℓy := −y ′′ + qy = λy on the intervals (−a, 0) and (0, b) with a, b > 0 and q ∈ L 2 (−a, b). We impose boundary conditions y(−a) cos α = y ′ (−a) sin α, y(b) cos β = y ′ (b) sin β, where α ∈ [0, π) and β ∈ (0, π], together with transmission conditions rationally-dependent on the eigenparameter viawith bi, aj > 0 for i = 1, . . . , N, and j = 1, . . . , M . Here we take η, κ ≥ 0 and N, M ∈ N0. The geometric multiplicity of the eigenvalues is considered and the cases in which the multiplicity can be 2 are characterized. An example is given to illustrate the cases. A Hilbert space formulation of the above eigenvalue problem as a self-adjoint operator eigenvalue problem in L 2 (−a, b) C N * C M * , for suitable N * , M * , is given. The Green's function and the resolvent of the related Hilbert space operator are expressed explicitly.Mathematics Subject Classification (2010). Primary 34B24; Secondary 34A36, 34B07.

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Spectral properties for discontinuous Dirac system with eigenparameter‐dependent boundary condition

Zheng,

Li,

Zheng

2024

Math Methods in App Sciences

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In this paper, Dirac system with interface conditions and spectral parameter dependent boundary conditions is investigated. By introducing a new Hilbert space, the original problem is transformed into an operator problem. Then the continuity and differentiability of the eigenvalues with respect to the parameters in the problem are showed. In particular, the differential expressions of eigenvalues for each parameter are given. These results would provide theoretical support for the calculation of eigenvalues of the corresponding problems.

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Inverse spectral problem for non-selfadjoint Dirac operator with boundary and jump conditions dependent on the spectral parameter

Abstract: Please cite this article as: Z. Wei, G. Wei, Inverse spectral problem for non-selfadjoint dirac operator with boundary and jump conditions dependent on the spectral parameter, Journal of Computational and Applied Mathematics (2016), http://dx.

Cited by 12 publications

References 17 publications

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

Sturm–Liouville Problems with Transfer Condition Herglotz Dependent on the Eigenparameter: Hilbert Space Formulation

Spectral properties for discontinuous Dirac system with eigenparameter‐dependent boundary condition

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