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9eeb9c7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | import OAI.Analysis.IrrationalRotation.Model.FieldDiagonal
namespace OAI
noncomputable section
open MeasureTheory
namespace Invariant233.WeightedShift
variable {X : Type*} [MeasurableSpace X] {μ : Measure X}
def fieldOperator (a : X → Weight) (C : ℝ) (hC : 0 ≤ C)
(ha : ∀ x, ‖a x‖ ≤ C)
(hm : ∀ k, AEStronglyMeasurable (fun x => a x k) μ) :
Lp Hilbert 2 μ →L[ℂ] Lp Hilbert 2 μ :=
(shift 1).toLinearIsometry.toContinuousLinearMap.compLpL 2 μ *
fieldDiagonal a C hC ha hm
def fieldTailProjection (m : ℤ) : Lp Hilbert 2 μ →L[ℂ] Lp Hilbert 2 μ :=
(tailProjection m).compLpL 2 μ
end Invariant233.WeightedShift
end
end OAI
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