A version of Gordon's theorem for multi-dimensional Schrödinger operators

We consider discrete Schrödinger operators in H = Δ + V in ℓ^2(Z^d) with d ≥ 1, and study the eigenvalue problem for these operators. It is shown that the point spectrum is empty if the potential V is sufficiently well approximated by periodic potentials. This criterion is applied to quasiperiodic V and to so-called Fibonacci-type superlattices.