Summary: We study the spectral properties of one-dimensional whole-line Schrödinger operators, especially those with Sturmian potentials. Building upon the Jitomirskaya-Last extension of the Gilbert-Pearson theory of subordinacy, we demonstrate 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.
Parts I, II, cf. Commun. Math. Phys. 207, No. 3, 687-696 (1999; Zbl 0962.81012) and Lett. Math. Phys. 50, No. 4, 245-257 (1999; Zbl 1044.81036).