Damanik D.
Continuity properties of one-dimensional quasicrystals
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ABSTRACT. We apply the Jitomirskaya-Last extension of the Gilbert-Pearson theory
to discrete one-dimensional Schr\"odinger 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
$\alpha > 0$ such that the corresponding operator has purely
$\alpha$-continuous spectrum. This result follows from uniform upper
and lower bounds for the $\| \cdot \|_L$-norm of the solutions
corresponding to energies from
the spectrum of the operator.