We study the spectral properties of one-dimensional whole-line Schrodinger
operators, especially those with Sturmian potentials. Building upon the Jit
omirskaya-Last extension of the Gilbert-Pearson theory of subordinacy, we d
emonstrate how to establish alpha- continuity of a whole-line operator from
power-law bounds on the solutions on a half-line. However, we require that
these bounds hold uniformly in the boundary condition.
We are able to prove these bounds for Sturmian potentials with rotation num
bers of bounded density and arbitrary coupling constant. From this we estab
lish purely alpha-continuous spectrum uniformly for all phases.
Our analysis also permits us to prove that the point spectrum is empty for
all Sturmian potentials.