Non-tangential
limit of the Weyl m-functions
for the ergodic Schrödinger equation
with Rafael Obaya,
J. Dynam. Differential Equations 10
(1998), 209-257.
This
paper deals with the spectral and qualitative problems associated with
the
one-dimensional ergodic Schrödinger equation. Let A2
be the set of those
energies
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 L1-topology
is
proved. As a consequence, it turns out that the
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.
