Operators with zero dimensional spectral measures appear naturally in the theory of ergodic Schrödinger operators. We develop concept a complete family Hausdorff measure functions order to analyze and distinguish between these any desired precision.We prove that dimension half-line operators positive upper Lyapunov exponent are at most logarithmic for every possible boundary phase. show this is...

Abstract We obtain spectral inequalities and asymptotic formulae for the discrete spectrum of operator $$\frac{1}{2}\, \log (-\Delta )$$ 1 2 log ( - ? ) </mm...