Spectral properties of one dimensional quasi-crystals

Abstract

In this paper we prove that the one dimensional Schrödinger operator on l2(ℤ) with potential given by: {Mathematical expression} has a Cantor spectrum of zero Lebesgue measure for any irrational α and any λ>0. We can thus extend the Kotani result on the absence of absolutely continuous spectrum for this model, to all {Mathematical expression}. © 1989 Springer-Verlag.