Hölder Continuity of Spectral Measures for the Finitely Differentiable Quasi-Periodic Schrödinger Operators

Abstract

In the present paper, we prove the $\frac{1}{2}$-Hölder continuity of spectral measures for the $C^{k}$ Schrödinger operators. This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrödinger cocycles in [5].