Continuous quasiperiodic Schrdinger operators with Gordon type potentials

Let us concern the quasi-periodic Schr"odinger operator in the continuous case, \begin{equation*} (Hy)(x)=-y^{primeprime}(x)+V(x,omega x)y(x), end{equation*} where $V:(R/)^2 o R$ is piecewisely $gamma$-H"older continuous with respect to the second variable. Let $L(E)$ be the Lyapunov exponent of $Hy=Ey$. Define $\beta(omega)$ as \begin{equation*} \beta(omega)= limsup_{k o infty}frac{-ln ||komega||}{k}. end{equation*} We prove that $H$ admits no eigenvalue in regime ${EinR:L(E)

Continuous quasiperiodic Schrdinger operators with Gordon type potentials Institutional Repository Document