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We study the almost Mathieu operator (h λ,α,θ u)(n) = u(n + 1) + u(n − 1) + λ cos(παn + θ)u(n) on 2 (Z), and prove that the dual of point spectrum is absolutely continuous spectrum. We use this to show that for λ = 2 it has purely singular continuous spectrum for a.e. pairs (α, θ). The α's for which we prove this are explicit. Our main goal in this paper is(More)
We study the class of general step-down multiple testing procedures, which contains the usually considered procedures determined by a nondecreasing sequence of thresholds (we call them threshold step-down, or TSD, procedures) as a parametric subclass. We show that all procedures in this class satisfying the natural condition of monotonicity and controlling(More)
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