Prove2Me

`BookProof.MixedLinearEsa.potMomOp_symmetric` (W : V → ℝ) (hW : Function.HasTemperateGrowth W) (m : V) : SymmetricOn (schwartzDomain V) (opL2 (potMomOp W m))

Proved
BookProof.MixedLinearEsa.potMomOp_symmetric

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMixedLinearEsa.

BookProof.MixedLinearEsa.potMomOp_symmetric (W : V → ℝ) (hW : Function.HasTemperateGrowth W) (m : V) : SymmetricOn (schwartzDomain V) (opL2 (potMomOp W m))

Formalization note: Lean 4 identifier BookProof.MixedLinearEsa.potMomOp_symmetric.

Preamble
-- Generated from ChapterMixedLinearEsa.lean — theorem BookProof.MixedLinearEsa.potMomOp_symmetric
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterMixedLinearEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterFourierMultiplierEsa
import Definitions.Def_ChapterStrichartzWave
import Definitions.Def_ChapterWaveUnboundedPotential
open BookProof.FourierMultiplierEsa
open BookProof.StrichartzWave
open BookProof.MixedLinearEsa



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace LineDeriv
open BookProof.StrichartzWave BookProof.FourierMultiplierEsa BookProof.FarisLavine

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]
Formal statement
theorem BookProof.MixedLinearEsa.potMomOp_symmetric (W : V → ℝ) (hW : Function.HasTemperateGrowth W) (m : V) :
    SymmetricOn (schwartzDomain V) (opL2 (potMomOp W m)) := by sorry

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