Gap Labelling for Almost Periodic Sturm-Liouville Operators

Published 26 Jan 2026 in math.SP and math.DS | (2601.18312v1)

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.

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