Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach

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Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach. / Judge, E.; Naboko, S.; Wood, I.

In: Journal of Difference Equations and Applications, Vol. 24, No. 8, 03.08.2018, p. 1247-1272.

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

Author

Judge, E. ; Naboko, S. ; Wood, I. / Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach. In: Journal of Difference Equations and Applications. 2018 ; Vol. 24, No. 8. pp. 1247-1272.

BibTeX

@article{ae90cbc216d643ba8b0bae894ffbe780,

title = "Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach",

abstract = "We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the essential spectrum of the discrete Schr{\"o}dinger operator. For periodic Jacobi operators we relax the rational dependence conditions on the values of the quasi-momenta from this previous work. We then explore conditions that permit not just the existence of infinitely many subordinate solutions to the formal spectral equation but also the embedding of infinitely many eigenvalues.",

keywords = "embedded eigenvalues, Jacobi matrices, periodic operators, spectral theory, Wigner-von Neumann, HETEROSTRUCTURES, SUBORDINACY, POTENTIALS, BOUND-STATES, MATRICES, CONTINUUM, SPECTRUM, SCHRODINGER-OPERATORS",

author = "E. Judge and S. Naboko and I. Wood",

year = "2018",

month = aug,

day = "3",

doi = "10.1080/10236198.2018.1468890",

language = "English",

volume = "24",

pages = "1247--1272",

journal = "Journal of Difference Equations and Applications",

issn = "1023-6198",

publisher = "Taylor & Francis",

number = "8",

}

RIS

TY - JOUR

T1 - Embedded eigenvalues for perturbed periodic Jacobi operators using a geometric approach

AU - Judge, E.

AU - Naboko, S.

AU - Wood, I.

PY - 2018/8/3

Y1 - 2018/8/3

N2 - We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the essential spectrum of the discrete Schrödinger operator. For periodic Jacobi operators we relax the rational dependence conditions on the values of the quasi-momenta from this previous work. We then explore conditions that permit not just the existence of infinitely many subordinate solutions to the formal spectral equation but also the embedding of infinitely many eigenvalues.

AB - We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the essential spectrum of the discrete Schrödinger operator. For periodic Jacobi operators we relax the rational dependence conditions on the values of the quasi-momenta from this previous work. We then explore conditions that permit not just the existence of infinitely many subordinate solutions to the formal spectral equation but also the embedding of infinitely many eigenvalues.

KW - embedded eigenvalues

KW - Jacobi matrices

KW - periodic operators

KW - spectral theory

KW - Wigner-von Neumann

KW - HETEROSTRUCTURES

KW - SUBORDINACY

KW - POTENTIALS

KW - BOUND-STATES

KW - MATRICES

KW - CONTINUUM

KW - SPECTRUM

KW - SCHRODINGER-OPERATORS

UR - http://www.scopus.com/inward/record.url?scp=85046636373&partnerID=8YFLogxK

U2 - 10.1080/10236198.2018.1468890

DO - 10.1080/10236198.2018.1468890

M3 - Article

AN - SCOPUS:85046636373

VL - 24

SP - 1247

EP - 1272

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 8

ER -

ID: 36461944