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The coexistence problem for the discrete Mathieu operator. (English) Zbl 0669.34016

We solve the coexistence problem for the periodic discrete Mathieu operator in all parametric cases. The main tool in the proof is Bezout’s theorem for projective plane curves. As an additional result we obtain the gap opening and gap growth powers for this operator.

MSC:

34A30 Linear ordinary differential equations and systems
47E05 General theory of ordinary differential operators
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