We study the spectral properties of Schrödinger operators on perturbed lattices. We shall
prove the non-existence or the discreteness of embedded eigenvalues, the limiting …

We consider a family of the discrete Schrödinger operators H λ μ, depending on two
parameters, in the d-dimensional lattice with a potential constructed via the delta function …

We consider a family of the discrete Schrödinger operators H_ λ μ, depending on
parameters, in the 3-dimensional lattice, Z^ 3 with a non-local potential constructed via the …

In this paper, we introduce a multi-dimensional generalization of Kitagawa's split-step
discrete-time quantum walk, study the spectrum of its evolution operator for the case of one …

Eigenvalue behaviours of Schrödinger operator defined on n-dimensional lattice with n+ 1
delta potentials are studied. It can be shown that lower threshold eigenvalue and lower …

arXiv:1208.4428v2 [math.SP] 24 Jul 2013 Page 1 arXiv:1208.4428v2 [math.SP] 24 Jul 2013 A
RELLICH TYPE THEOREM FOR DISCRETE SCHRODINGER OPERATORS HIROSHI …

The displacement field near a tip of a finite crack, due to the diffraction of a wave on a square
lattice, is studied. The finite section method, in the theory of Toeplitz operators on \ell_2, is …

The displacement field, due to diffraction of a time harmonic lattice wave on square lattice,
near the tip of a semi-infinite rigid constraint is investigated. A rigorous proof, supported by …

We study the inverse scattering for Schrödinger operators on locally perturbed periodic
lattices. We show that the associated scattering matrix is equivalent to the Dirichlet-to …

We address the Laplacian on a perturbed periodic graph which might not be a periodic
graph. We give a criterion for the essential spectrum of the Laplacian on the perturbed graph …