OAI/NumberTheory/Ostmann/Arithmetic/BulkKernelIntegralComparison.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

1. theorem OAI.Ostmann.BulkIntegrand.integral_comparison line 12
2. theorem OAI.Ostmann.PublishedProgressionInput.bulk_kernel_integral_comparison line 29

   Source documentation

   The published progression input compares the sharp paired kernel in the actual selected coordinates, while every nonbulk coordinate remains fixed. There is no assumption about a previously integrated slice.

   theorem PublishedProgressionInput.bulk_kernel_integral_comparison
       (P : PublishedProgressionInput) {σ : Type*} [Fintype σ] {k n : ℕ}
       (base : σ → ℝ) (S : Finset σ) (e : Fin k ↪ σ) (he : ∀ i, e i ∈ S)
       (childBound pivotBound : ℕ → ℕ) (T : Bool → MovingSlotData σ n)
       (hT : ∀ b i, (T b).CompensationAbsent (e i))
       (ψ : 𝓢(ℝ, ℂ)) (X lo hi V : ℝ) (hlo : 1 ≤ lo) (hhi : lo ≤ hi)
       (hV : ∀ b, (T b).Frequencies (fun s => |(s : ℝ)| ≤ V))
       (φ : ℝ → ℝ) (G : ℕ → ℝ) (B D : ℝ) (hB : 0 ≤ B) (hD : 0 ≤ D)
       (hφ : ∀ x, |φ x| ≤ B) (hlip : ∀ x y, |φ x - φ y| ≤ D * |x - y|)
       (hout : ∀ x, 1 ≤ |x| → φ x = 0)
       (d r : ℕ) (hsize : ∀ b, (T b).SizeLE d) (hregular : ∀ b, (T b).RegularLengthLE r)
       (L R : ℝ) (f : BulkIntegrand σ)
   …

   Mentions: OAI.Ostmann.PublishedProgressionInput, OAI.Ostmann.MovingSlotData, OAI.Ostmann.BulkIntegrand