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On the spectrum of the one-dimensional Schrödinger operator

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  • The spectral theory of the one-dimensional Schrödinger operator with a quasi-periodic potential can be fruitfully studied considering the corresponding differential system. In fact the presence of an exponential dichotomy for the system is equivalent to the statement that the energy $E$ belongs to the resolvent of the operator. Starting from results already obtained for the spectrum in the continuous case, we show that in the discrete case a generic bounded measurable Schrödinger cocycle has Cantor spectrum.
    Mathematics Subject Classification: Primary: 34D08, 34D09; Secondary: 37B55.

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