α-Continuity Properties of One-Dimensional Quasicrystals

Abstract:

We apply the Jitomirskaya-Last extension of the Gilbert-Pearson theory to discrete one-dimensional Schrödinger operators with potentials arising from generalized Fibonacci sequences. We prove for certain rotation numbers that for every value of the coupling constant, there exists an α > 0 such that the corresponding operator has purely α-continuous spectrum. This result follows from uniform upper and lower bounds for the ∥⋅∥_L-norm of the solutions corresponding to energies from the spectrum of the operator.