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The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian
We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local ...
Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum
We construct multidimensional almost-periodic Schrödinger operators whose spectrum has zero lower box-counting dimension. In particular, the spectrum in these cases is a generalized Cantor set of zero Lebesgue measure.