{kappa : Fin D → ℝ} {km : ℝ} (hkm : 0 ≤ km) (hk : ∀ j, |kappa j| ≤ km) (p : MvPolynomial (Fin D) ℂ) : ‖pgLp (∑ j : Fin D, ((kappa j : ℝ) : ℂ) • coreD j (coreD j p))‖ ≤...

Proved

BookProof.GaussCoreQuadBounds.norm_weighted_kin_le

by leonardopedro · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

Lean 4 theorem BookProof.GaussCoreQuadBounds.norm_weighted_kin_le (module BookProof.GaussCoreQuadBounds), source chapter BookProof/ChapterGaussCoreQuadBounds.lean.

Preamble

-- Generated from ChapterGaussCoreQuadBounds.lean — theorem BookProof.GaussCoreQuadBounds.norm_weighted_kin_le
import Mathlib
import Definitions.Def_ChapterGaussCoreQuadBounds
open BookProof.GaussCoreQuadBounds








open Finset MvPolynomial
open BookProof.HermiteProductCore BookProof.QgHermiteCore BookProof.QgHermiteFriedrichs
open BookProof.FarisLavine

noncomputable section

variable {D : ℕ}

Formal statement

theorem BookProof.GaussCoreQuadBounds.norm_weighted_kin_le {kappa : Fin D → ℝ} {km : ℝ} (hkm : 0 ≤ km)
    (hk : ∀ j, |kappa j| ≤ km) (p : MvPolynomial (Fin D) ℂ) :
    ‖pgLp (∑ j : Fin D, ((kappa j : ℝ) : ℂ) • coreD j (coreD j p))‖
      ≤ km * ‖pgLp (kinPoly p)‖ := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterGaussCoreQuadBounds.lean

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