OAI/Analysis/LipschitzHilbert/Trees/SourceCentralBudget.lean

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The mass and measure bounds in §11 give the precise power of N in the central estimate. The previously proved exponent gain then absorbs all of the fixed polynomial factors.

  1. theorem OAI.LipschitzHilbert.central_root_budget line 16
  2. theorem OAI.LipschitzHilbert.source_central_estimate line 61
  3. theorem OAI.LipschitzHilbert.eventually_source_central_integral_gain line 95

    Source documentation

    The actual source phase and shift count give the central negative-power estimate once the normalized vertex moment has been established.

    theorem eventually_source_central_integral_gain (d q Q : ℝ)
    (hd : 0 ≤ d) (hq : 0 ≤ q) (hQ : 0 ≤ Q) :
    ∀ᶠ L : ℝ in atTop, ∀ D : ℝ, 1 ≤ D → D ≤ L^d →
    ∀ (X κ : Type*) [MeasurableSpace X] [Fintype κ]
      (μ : Measure X) [IsFiniteMeasure μ] (n : X → ℝ) (amp : X → EuclideanSpace ℂ κ)
      (N F S : ℝ), 0 < N → 0 < F → 0 ≤ S → L/2 ≤ Real.log N →
    let p := Real.sqrt L
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