TY - JOUR

T1 - Eigenvalues of periodic difference operators on lattice octants

AU - Korotyaev, Evgeny

N1 - Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/8/1

Y1 - 2021/8/1

N2 - Consider a difference operator H with periodic coefficients on the octant of the lattice. We show that for any integer N and any bounded interval I, there exists an operator H having N eigenvalues, counted with multiplicity on this interval, and does not exist other spectra on the interval. Also right and to the left of it are spectra and the corresponding subspaces have an infinite dimension. Moreover, we prove similar results for other domains and any dimension. The proof is based on the inverse spectral theory for periodic Jacobi operators.

AB - Consider a difference operator H with periodic coefficients on the octant of the lattice. We show that for any integer N and any bounded interval I, there exists an operator H having N eigenvalues, counted with multiplicity on this interval, and does not exist other spectra on the interval. Also right and to the left of it are spectra and the corresponding subspaces have an infinite dimension. Moreover, we prove similar results for other domains and any dimension. The proof is based on the inverse spectral theory for periodic Jacobi operators.

KW - Discrete Schrödinger operator

KW - Eigenvalues

KW - Lattice

KW - LAPLACIAN

KW - Discrete Schrodinger operator

KW - ZIGZAG NANORIBBONS

KW - SPECTRAL PROPERTIES

KW - SCHRODINGER-OPERATORS

UR - http://www.scopus.com/inward/record.url?scp=85102575392&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2021.125138

DO - 10.1016/j.jmaa.2021.125138

M3 - Article

AN - SCOPUS:85102575392

VL - 500

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 125138

ER -