On the number of eigenvalues of the discrete one-dimensional Schrödinger operator with a complex potential

Hulko, Artem

doi:10.1007/s13373-016-0093-2

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…the difference operators like discrete Schrödinger or discrete Dirac operators with complex potentials. The authors are only aware of [26] which is focused on the number rather than the location of eigenvalues for the discrete Schrödinger operator with a complex potential and a related work [28] for the cubic lattice. Some constrains on the location of the discrete spectrum of semi-infinite complex Jacobi matrices are discussed in [15].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Spectral Enclosures for Non-self-adjoint Discrete Schrödinger Operators

Ibrogimov

Štampach

2019

Integr. Equ. Oper. Theory

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We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex p -potentials for 1 ≤ p ≤ ∞. In the case of 1 -potentials, the derived bound is shown to be optimal. For p > 1, two different spectral bounds are obtained. The method relies on the Birman-Schwinger principle and various techniques for estimations of the norm of the Birman-Schwinger operator. V e n := υ n e n , ∀n ∈ Z.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Spectral Enclosures for Non-self-adjoint Discrete Schrödinger Operators

Ibrogimov

Štampach

2019

Integr. Equ. Oper. Theory

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Bounds for Schrödinger Operators on the Half-Line Perturbed by Dissipative Barriers

Stepanenko

2021

Integr. Equ. Oper. Theory

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We consider Schrödinger operators of the form $$H_R = - \,\text {{d}}^2/\,\text {{d}}x^2 + q + i \gamma \chi _{[0,R]}$$ H R = - d 2 / d x 2 + q + i γ χ [ 0 , R ] for large $$R>0$$ R > 0 , where $$q \in L^1(0,\infty )$$ q ∈ L 1 ( 0 , ∞ ) and $$\gamma > 0$$ γ > 0 . Bounds for the maximum magnitude of an eigenvalue and for the number of eigenvalues are proved. These bounds complement existing general bounds applied to this system, for sufficiently large R.

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On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

Hulko

2018

Anal.Math.Phys.

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On the number of eigenvalues of the discrete one-dimensional Schrödinger operator with a complex potential

Abstract: We study the eigenvalues of the discrete Schrödinger operator with a complex potential. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.

Cited by 6 publications

References 22 publications

Spectral Enclosures for Non-self-adjoint Discrete Schrödinger Operators

Spectral Enclosures for Non-self-adjoint Discrete Schrödinger Operators

Bounds for Schrödinger Operators on the Half-Line Perturbed by Dissipative Barriers

On the number of eigenvalues of the discrete one-dimensional Dirac operator with a complex potential

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