| 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 | |