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Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique. / Judge, Edmund; Naboko, Sergey; Wood, Ian.

In: Studia Mathematica, Vol. 242, No. 2, 01.01.2018, p. 179-215.

Research output: Contribution to journal › Article › peer-review

Harvard

Judge, E, Naboko, S & Wood, I 2018, 'Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique', Studia Mathematica, vol. 242, no. 2, pp. 179-215. https://doi.org/10.4064/sm170325-23-8

APA

Judge, E., Naboko, S., & Wood, I. (2018). Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique. Studia Mathematica, 242(2), 179-215. https://doi.org/10.4064/sm170325-23-8

Vancouver

Judge E, Naboko S, Wood I. Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique. Studia Mathematica. 2018 Jan 1;242(2):179-215. https://doi.org/10.4064/sm170325-23-8

Author

Judge, Edmund ; Naboko, Sergey ; Wood, Ian. / Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique. In: Studia Mathematica. 2018 ; Vol. 242, No. 2. pp. 179-215.

BibTeX

@article{8dc190ab5dc040b69d1de885762a80a9,
title = "Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique",
abstract = "For an arbitrary Hermitian period-T Jacobi operator, we assume a per- turbation by a Wigner{von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, S, of the spectral parameter. We employ discrete Levinson type techniques to achieve this, which allow the analysis of the asymptotic behaviour of the solutions. This enables us to construct infinitely many spectral singularities on the absolutely continuous spectrum of the periodic Jacobi opera- tor, which are stable with respect to an l1-perturbation. An analogue of the quantisation conditions from the continuous case appears, relating the frequency of the oscillation of the potential to the quasi-momentum associated with the purely periodic operator.",
keywords = "Jacobi operators, Levinson techniques, Periodic operators, Subordinate solutions, Wigner-von Neumann potentials",
author = "Edmund Judge and Sergey Naboko and Ian Wood",
year = "2018",
month = jan,
day = "1",
doi = "10.4064/sm170325-23-8",
language = "English",
volume = "242",
pages = "179--215",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",
number = "2",

}

RIS

TY - JOUR

T1 - Spectral results for perturbed periodic Jacobi matrices using the discrete Levinson technique

AU - Judge, Edmund

AU - Naboko, Sergey

AU - Wood, Ian

PY - 2018/1/1

Y1 - 2018/1/1

N2 - For an arbitrary Hermitian period-T Jacobi operator, we assume a per- turbation by a Wigner{von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, S, of the spectral parameter. We employ discrete Levinson type techniques to achieve this, which allow the analysis of the asymptotic behaviour of the solutions. This enables us to construct infinitely many spectral singularities on the absolutely continuous spectrum of the periodic Jacobi opera- tor, which are stable with respect to an l1-perturbation. An analogue of the quantisation conditions from the continuous case appears, relating the frequency of the oscillation of the potential to the quasi-momentum associated with the purely periodic operator.

AB - For an arbitrary Hermitian period-T Jacobi operator, we assume a per- turbation by a Wigner{von Neumann type potential to devise subordinate solutions to the formal spectral equation for a (possibly infinite) real set, S, of the spectral parameter. We employ discrete Levinson type techniques to achieve this, which allow the analysis of the asymptotic behaviour of the solutions. This enables us to construct infinitely many spectral singularities on the absolutely continuous spectrum of the periodic Jacobi opera- tor, which are stable with respect to an l1-perturbation. An analogue of the quantisation conditions from the continuous case appears, relating the frequency of the oscillation of the potential to the quasi-momentum associated with the purely periodic operator.

KW - Jacobi operators

KW - Levinson techniques

KW - Periodic operators

KW - Subordinate solutions

KW - Wigner-von Neumann potentials

UR - http://www.scopus.com/inward/record.url?scp=85044227230&partnerID=8YFLogxK

U2 - 10.4064/sm170325-23-8

DO - 10.4064/sm170325-23-8

M3 - Article

AN - SCOPUS:85044227230

VL - 242

SP - 179

EP - 215

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 2

ER -

ID: 36462453