| import OAI.Analysis.IrrationalRotation.Model.WeightedShift | |
| import Mathlib.Analysis.Fourier.AddCircle | |
| import Mathlib.MeasureTheory.Function.LpSpace.Basic | |
| namespace OAI | |
| noncomputable section | |
| open MeasureTheory | |
| namespace Invariant233.DiagonalGauge | |
| abbrev Circle := AddCircle (1 : ℝ) | |
| abbrev Fiber := WeightedShift.Hilbert | |
| def weight (t : Circle) : WeightedShift.Weight := | |
| ⟨fun k => fourier k t, memℓp_infty <| by | |
| refine ⟨1, ?_⟩ | |
| rintro r ⟨k, rfl⟩ | |
| exact (Circle.norm_coe _).le⟩ | |
| def fiberOperator (t : Circle) : Fiber →L[ℂ] Fiber := | |
| WeightedShift.diagonal (weight t) | |
| def fieldOperator {X : Type*} [MeasurableSpace X] (μ : Measure X) (t : Circle) : | |
| Lp Fiber 2 μ →L[ℂ] Lp Fiber 2 μ := | |
| (fiberOperator t).compLpL 2 μ | |
| def conjugate {X : Type*} [MeasurableSpace X] (μ : Measure X) | |
| (A : Lp Fiber 2 μ →L[ℂ] Lp Fiber 2 μ) (t : Circle) : | |
| Lp Fiber 2 μ →L[ℂ] Lp Fiber 2 μ := | |
| fieldOperator μ t * A * fieldOperator μ (-t) | |
| end Invariant233.DiagonalGauge | |
| end | |
| end OAI | |