Half-line eigenfunction estimates and stability of singular continuous spectrum
نویسنده
چکیده
We consider discrete one-dimensional Schrödinger operators with strictly ergodic, aperiodic potentials taking finitely many values. The well-known tendency of these operators to have purely singular continuous spectrum of zero Lebesgue measure is further elucidated. We study stability of singular continuity with respect to local perturbations. Moreover, we provide a unified approach to both the study of the spectral type as well as the measure of the spectrum as a set. We apply this approach to Schrödinger Operators with Sturmian potentials. Finally, in the appendix, we discuss the two different strictly ergodic dynamical Systems associated to a circle map.
منابع مشابه
Half-line eigenfunction estimates and singular continuous spectrum of zero Lebesgue measure
We consider discrete one-dimensional Schrödinger operators with strictly ergodic, aperiodic potentials taking finitely many values. The well-known tendency of these operators to have purely singular continuous spectrum of zero Lebesgue measure is further elucidated. We provide a unified approach to both the study of the spectral type as well as the measure of the spectrum as a set. We apply thi...
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تاریخ انتشار 2008