| import OAI.Analysis.IrrationalRotation.Model.SawtoothSmoothing | |
| import Mathlib.Topology.Instances.AddCircle.Defs | |
| namespace OAI | |
| noncomputable section | |
| namespace InvariantProjection.Continuity | |
| def circleSmoothSawtooth (δ : ℝ) : AddCircle (1 : ℝ) → ℝ := | |
| AddCircle.liftIco 1 0 (smoothSawtooth δ) | |
| def circleSmoothedDrop (C a δ : ℝ) (x : AddCircle (1 : ℝ)) : ℝ := | |
| C * (a + circleSmoothSawtooth δ x - circleSmoothSawtooth δ (x + (a : AddCircle (1 : ℝ)))) | |
| def circleSmoothingTransfer (C δ : ℝ) (x : AddCircle (1 : ℝ)) : ℝ := | |
| C * (circleSmoothSawtooth δ x - (AddCircle.equivIco 1 0 x : ℝ)) | |
| end InvariantProjection.Continuity | |
| end | |
| end OAI | |