`BookProof.ScalaronHermiteEsa.integrable_pgFun_mul_of_gaussExpDecay` {u : Vd d → ℂ} (hu : GaussExpDecay u) (p : MvPolynomial (Fin d) ℂ) : Integrable (fun x : Vd d => pgFun p x * u

Proved

BookProof.ScalaronHermiteEsa.integrable_pgFun_mul_of_gaussExpDecay

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalaronHermiteEsa.

BookProof.ScalaronHermiteEsa.integrable_pgFun_mul_of_gaussExpDecay {u : Vd d → ℂ} (hu : GaussExpDecay u) (p : MvPolynomial (Fin d) ℂ) : Integrable (fun x : Vd d => pgFun p x * u x)

Formalization note: Lean 4 identifier BookProof.ScalaronHermiteEsa.integrable_pgFun_mul_of_gaussExpDecay.

Preamble

-- Generated from ChapterScalaronHermiteEsa.lean — theorem BookProof.ScalaronHermiteEsa.integrable_pgFun_mul_of_gaussExpDecay
import Definitions.Def_ChapterQgHermiteCore
import Definitions.Def_ChapterQgHermiteFriedrichs
import Definitions.Def_ChapterQgHermiteOscillatorEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterScalaronHermiteEsa
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.ScalaronHermiteEsa



open MeasureTheory Complex MvPolynomial FourierTransform
open BookProof.HermiteProductCore BookProof.QgHermiteCore BookProof.QgHermiteFriedrichs
open BookProof.QgHermiteOscillator BookProof.FarisLavine BookProof.Starobinsky
open BookProof.StoneBridge BookProof.EsaClosure BookProof.ChapterStoneResolvent

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.ScalaronHermiteEsa.integrable_pgFun_mul_of_gaussExpDecay {u : Vd d → ℂ} (hu : GaussExpDecay u)
    (p : MvPolynomial (Fin d) ℂ) : Integrable (fun x : Vd d => pgFun p x * u x) := by sorry

View graph