From 55653f7add3f01550a5993a6f529ec84c85a2b82 Mon Sep 17 00:00:00 2001 From: Floris van Doorn Date: Fri, 19 Apr 2024 09:42:43 +0200 Subject: [PATCH] remove classical file --- Carleson/Classical.lean | 30 ------------------------------ 1 file changed, 30 deletions(-) delete mode 100644 Carleson/Classical.lean diff --git a/Carleson/Classical.lean b/Carleson/Classical.lean deleted file mode 100644 index 41eba024..00000000 --- a/Carleson/Classical.lean +++ /dev/null @@ -1,30 +0,0 @@ -import Carleson.Carleson -import Mathlib.Analysis.Fourier.AddCircle - -/-! The classical version of Carleson's theorem. - -For this we take `X = ℝ`, `K x y := 1 / (x - y)` and `Θ = {linear functions}`. --/ - -open MeasureTheory Measure NNReal Metric Complex Set TileStructure Function BigOperators Filter -open AddCircle Topology -open scoped ENNReal -noncomputable section - -variable {T : ℝ} {f : AddCircle T → ℂ} {ε : ℝ} [Fact (0 < T)] - - -def partialFourierSum (f : AddCircle T → ℂ) (n : ℤ) (x : AddCircle T) : ℂ := - ∑ i in Finset.Icc (- n) n, fourierCoeff f i * fourier i x - -theorem classical_carleson (hf : UniformContinuous f) (h2f : ∀ x, ‖f x‖ ≤ 1) - (hε : 0 < ε) : - ∃ (E : Set (AddCircle T)) (N₀ : ℕ), MeasurableSet E ∧ haarAddCircle E ≤ .ofReal ε ∧ - ∀ N x, N₀ ≤ N → x ∉ E → ‖f x - partialFourierSum f N x‖ < ε := by - sorry - - -theorem classical_carleson_pointwise (hf : UniformContinuous f) (h2f : ∀ x, ‖f x‖ ≤ 1) : - ∃ (E : Set (AddCircle T)) (N₀ : ℕ), MeasurableSet E ∧ haarAddCircle E = 0 ∧ - ∀ x, x ∉ E → Tendsto (partialFourierSum f · x) atTop (𝓝 (f x)) := by - sorry