Eigenvalues of periodic difference operators on lattice octant
Spectral Theory
2019-04-30 v1 Analysis of PDEs
Abstract
Consider a difference operator with periodic coefficients on the octant of the lattice. We show that for any integer and any bounded interval , there exists an operator having 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.
Cite
@article{arxiv.1904.12109,
title = {Eigenvalues of periodic difference operators on lattice octant},
author = {Evgeny Korotyaev},
journal= {arXiv preprint arXiv:1904.12109},
year = {2019}
}
Comments
2 figures, 17 pages. arXiv admin note: text overlap with arXiv:1712.08893