OAI/NumberTheory/CubicMoment/Estimates/HeightEndpointProfile.lean

GitHub source file

9 declarations, 0 contain sorry, 0 declared as axioms

A fixed compact profile removes the reciprocal singularity. Dilating this profile gives the normalized endpoint weights used in localization.

  1. def OAI.CubicFirstMoment.endpointProfile line 12
  2. lemma OAI.CubicFirstMoment.endpointProfile_eq line 16
  3. lemma OAI.CubicFirstMoment.heightWindow_dilation line 35
  4. lemma OAI.CubicFirstMoment.localizedEndpointWeight_dilation line 40
  5. def OAI.CubicFirstMoment.secondDerivativeBudget line 54
  6. lemma OAI.CubicFirstMoment.secondDerivativeBudget_pos line 57
  7. lemma OAI.CubicFirstMoment.norm_iteratedDeriv_le_budget line 64
  8. lemma OAI.CubicFirstMoment.scaled_schwartz_product_second_bound line 74

    Source documentation

    Only two derivatives are needed for the far-cell integration by parts.

    lemma scaled_schwartz_product_second_bound (f g : SchwartzMap ℝ ℂ) :
    ∃ K : ℝ, 0 < K ∧ ∀ a : ℝ, 0 ≤ a → a ≤ 1 → ∀ x : ℝ,
      ‖deriv (deriv (fun y => f (a*y)*g y)) x‖ ≤ K := by
…
  9. theorem OAI.CubicFirstMoment.localizedEndpointWeight_second_uniform line 107