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- W2036384201 abstract "Let H = −12 Δ + V on l2(Z), where V(x), xϵZ are i.i.d.r.v.'s with common probability distribution μ. Let h(t) = ∝ e−itvdμ(v), let N(E) be the integrated density of states, and let νE be the invariant measure at energy E. It is proven: 1. Let h be d-times differentiable on (0, + ∞) with bounded derivatives such that h(j)(t) → 0 as t → +∞ for j = 0, 1, …, d. Then: (i) N(E) is a Cd function. (ii) If d ⩾ 3, νE is absolutely continuous for all EϵR and dνEdx is of class C[(d − 1)2] − 1jointly in E and x. 2. Let h be differentiable on (0, +∞) with h(j)(t) = O(e−b¦t¦) for j = 0, 1 and some b > 0. Then dνEdx is jointly analytic in E and x." @default.
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- W2036384201 date "1990-01-01" @default.
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- W2036384201 title "Regularity of the invariant measure and of the density of states in the one-dimensional Anderson model" @default.
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