On the genericity of nonvanishing instability intervals in Hills equation

Abstract

We prove that for (Baire) almost every C’° periodic function V d2/dx2 + V has all its instability intervals non-empty. In the spectral theory of one dimensional Schrodinger operators [3] [10] with periodic potentials, a natural question occurs involving the presence of gaps in the spectrum. Let H = d2 2 + V on L2(R, d x) where V(x + 1) = V(x) for all x. Let… (More)

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