Abstract
We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, α, the measure of the spectrum,S(α, λ, ϑ)=|4–2|λ‖. For |λ|≠2 we show that if αn is rational and\(\alpha _n \to \alpha \) irrational, then\(S_ + (\alpha _n ,\lambda ,\theta ) \to |4 - 2|\lambda ||\).
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Communicated by T. Spencer
Dedicated to Res Jost and Arthur Wightman
Research partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325
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Avron, J., v. Mouche, P.H.M. & Simon, B. On the measure of the spectrum for the almost Mathieu operator. Commun.Math. Phys. 132, 103–118 (1990). https://doi.org/10.1007/BF02278001
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DOI: https://doi.org/10.1007/BF02278001