Some Schrodinger operators with power-decaying potentials and pure point spectrum, II. The discrete case

Abstract

We construct deterministic potentials V(n) = O(n(-c)) such that the discrete Schrodinger operator (Hy)(n) = y(n - 1) y(n 1) V(n)y(n) on l(2)(N) has dense pure point spectrum on [-2, 2] for almost all values of V(1). As a consequence of this construction, we also obtain power-decaying potentials for which the spectrum is purely singular continuous on (-2, 2) for all values of V(1).