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Gap Labelling for Almost Periodic Sturm-Liouville Operators

Gerald Teschl, Yifei Wang, Bing Xie, and Zhe Zhou

Abstract
In this paper, we introduce a rotation number for almost periodic Sturm-Liouville operators in the spirit of Johnson and Moser. We then prove the gap labelling theorem in terms of rotation numbers for the operator in question. To do this, we rigorously prove the almost periodicity of Green's functions.

MSC2020: Primary 34L05, 81Q10; Secondary 34B20, 34B27
Keywords: Sturm-Liouville operator, almost periodic function, rotation number, gap label.

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