Non-tangential limit of the Weyl m-functions for the ergodic Schrödinger equation

with Rafael Obaya,

J. Dynam. Differential Equations

This paper deals with the spectral and qualitative problems associated with the

one-dimensional ergodic Schrödinger equation. Let A

for which the real projective flow admits an invariant linear measure with square

integrable density function. On this set the directional derivative of the Floquet

coefficient is calculated and the existence of non-tangential limit of the Weyl

m-functions in the L

known Deift-Simon inequality for the derivative of the rotation number obtained

from Kotani's theory is in fact an equality. In the bounded orbit case, the uniform

boundedness of the Weyl m-functions is deduced and necessary and sufficient

conditions to ensure their uniform convergence are obtained.