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 study the exact solution of the two-body problem on a tight-binding one-dimensional
lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show …

We discuss the validity of the Weyl asymptotics—in the sense of two-sided bounds—for the
size of the discrete spectrum of (discrete) Schrödinger operators on the d-dimensional, d≥ …

We study the transport properties of Schr\"{o} dinger operators on $\mathbb {R}^ d $ and
$\mathbb {Z}^ d $ with potentials that are periodic in some directions and compactly …

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal
polynomials with Szegő asymptotics off the real axis. A key idea is to prove the equivalence …

In this paper, we consider discrete Schrödinger operators of the form, We view as a
perturbation of the free operator, where. For (no perturbation), and does not have …

We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with
analytic sampling functions by decaying potentials and seek decay conditions under which …

Half-line Schrödinger operators with no bound states Page 1 Acta Math., 193 (2004),
31-72 (~) 2004 by Institut Mittag-Leffler. All rights reserved Half-line SchrSdinger operators with …

We consider the discrete Laplacian Δ on the cubic lattice Z^d, and deduce estimates on the
group e^itΔ and the resolvent (Δ-z)^-1, weighted by ℓ^q(Z^d)-weights for suitable …

Consider the Schrödinger operators H±=-d 2/dx 2±V (x). We present a method for estimating
the potential in terms of the negative eigenvalues of these operators. Among the …