Continuous quasiperiodic Schrodinger operators with Gordon type potentials

Let us concern the quasi-periodic Schrodinger operator in the continuous case (Hy)(x) = -y '' (x) + V(x, omega x)y(x), where V:(R/Z)(2) -> R is piecewisely gamma-Holder continuous with respect to the second variable. Let L(E) be the Lyapunov exponent of Hy = Ey. Define beta(omega) as beta(omega) = lim sup(k ->infinity)-ln parallel to k omega parallel to/k. We prove that H admits no eigenvalue in regime {E is an element of R : L(E) < gamma beta(omega)}. Published by AIP Publishing.