Moments of Leb restricted to the intersection spectrum Σ_{α,λ} of the AMO are polynomials in λ with trigonometric-polynomial coefficients in α, implying continuous weak-* dependence of μ⁻_{α,λ} on parameters and analyticity in λ away from λ=1.
Shamis, Some connections between almost periodic and periodic discrete Schr¨ odinger operators with analytic potentials,Journal of Spectral Theory,1(2011), pp
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Generalized Aubry-Andr\'e formula and continuity of the intersection spectrum of the Almost Mathieu operator
Moments of Leb restricted to the intersection spectrum Σ_{α,λ} of the AMO are polynomials in λ with trigonometric-polynomial coefficients in α, implying continuous weak-* dependence of μ⁻_{α,λ} on parameters and analyticity in λ away from λ=1.