 97169 Damanik D.
 Continuity properties of onedimensional quasicrystals
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Apr 3, 97

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Abstract. We apply the JitomirskayaLast extension of the GilbertPearson theory
to discrete onedimensional 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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