{v : R → Fin D → ℝ} {B : ℝ} (hB0 : 0 ≤ B) (hB : ∀ x : Vd D, potFun v x ≤ B * ‖x‖ ^ 2) (p : MvPolynomial (Fin D) ℂ) : ‖pgLp (potPoly v * p)‖ ≤ 4 * B * ‖pgLp (harmPoly *...

Proved

BookProof.SqSumFarisLavine.norm_potPoly_mul_le

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

faris-lavinespectral-theorytimepiece

Lean 4 theorem BookProof.SqSumFarisLavine.norm_potPoly_mul_le (module BookProof.SqSumFarisLavine), source chapter BookProof/ChapterSqSumFarisLavine.lean.

Preamble

-- Generated from ChapterSqSumFarisLavine.lean — theorem BookProof.SqSumFarisLavine.norm_potPoly_mul_le
import Mathlib
import Definitions.Def_ChapterSqSumFarisLavine
open BookProof.SqSumFarisLavine












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

noncomputable section

variable {D : ℕ} {R : Type*} [Fintype R]

Formal statement

theorem BookProof.SqSumFarisLavine.norm_potPoly_mul_le {v : R → Fin D → ℝ} {B : ℝ} (hB0 : 0 ≤ B)
    (hB : ∀ x : Vd D, potFun v x ≤ B * ‖x‖ ^ 2) (p : MvPolynomial (Fin D) ℂ) :
    ‖pgLp (potPoly v * p)‖ ≤ 4 * B * ‖pgLp (harmPoly * p)‖ := by sorry

Source

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

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