Continuity of the Measure of the Spectrum for Quasiperiodic Schrödinger Operators with Rough Potentials
- Author(s): Jitomirskaya, S
- Mavi, R
- et al.
Published Web Locationhttps://doi.org/10.1007/s00220-013-1856-1
We study discrete quasiperiodic Schrödinger operators on ℓ2(ℤ) with potentials defined by γ-Hölder functions. We prove a general statement that for γ > 1/2 and under the condition of positive Lyapunov exponents, measure of the spectrum at irrational frequencies is the limit of measures of spectra of periodic approximants. An important ingredient in our analysis is a general result on uniformity of convergence from above in the subadditive ergodic theorem for strictly ergodic cocycles. © 2013 Springer-Verlag Berlin Heidelberg.