97-169 Damanik D.

Continuity properties of one-dimensional quasicrystals (23K, LaTeX) Apr 3, 97

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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.

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