OAI/Analysis/FourierLLogL/Thermal/Flat.lean

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1 declarations, 0 contain sorry, 0 declared as axioms

Selecting a flat coefficient

  1. lemma OAI.FourierLLogL.Dyadic.Thermal.flat_selection line 13

    Source documentation

    Find λ after the width estimate.

    lemma flat_selection (D : ℝ) (hD : 1 ≤ D) :
        ∀ᶠ j : ℕ in atTop, ∀ (M : ℕ) (A B : Form M), 0 ≤ A → 0 ≤ B →
          ∀ t : ℝ, t ≤ D*height j →
            F (A+long j • B)-F A ≤ 400*t →
          ∃ c : ℝ, height j * H j^200 ≤ c ∧ H j^140*c ≤ long j ∧
            flat (H j) (plateErr j) A (c • B) ∧
            F (A+c • B)-F A ≤ 400*t ∧
            (label (A+c • B)).Ex (form B) ≤ 400*t/c := by
    …

    Mentions: OAI.FourierLLogL.Dyadic.Thermal.Form, OAI.FourierLLogL.Dyadic.Thermal.F, OAI.FourierLLogL.Dyadic.Thermal.H, OAI.FourierLLogL.Dyadic.Thermal.flat, OAI.FourierLLogL.Dyadic.Thermal.plateErr, OAI.FourierLLogL.Dyadic.Thermal.label, OAI.FourierLLogL.Dyadic.Thermal.form