Prove2Me

`BookProof.StrichartzWave.wave_add_boundedPotentialOp_essentiallySelfAdjoint` (n : ℕ) (W : SpaceTime n → ℝ) (hW : Function.HasTemperateGrowth W) (hmem : MemLp (fun x => (W x : ℂ))

Proved
BookProof.StrichartzWave.wave_add_boundedPotentialOp_essentiallySelfAdjoint

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWaveUnboundedPotential.

BookProof.StrichartzWave.wave_add_boundedPotentialOp_essentiallySelfAdjoint (n : ℕ) (W : SpaceTime n → ℝ) (hW : Function.HasTemperateGrowth W) (hmem : MemLp (fun x => (W x : ℂ)) (⊤ : ℝ≥0∞) (volume : Measure (SpaceTime n))) : BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain (SpaceTime n)) (opL2 (waveOp n 0 + potentialOp W))

Formalization note: Lean 4 identifier BookProof.StrichartzWave.wave_add_boundedPotentialOp_essentiallySelfAdjoint.

Preamble
-- Generated from ChapterWaveUnboundedPotential.lean — theorem BookProof.StrichartzWave.wave_add_boundedPotentialOp_essentiallySelfAdjoint
import Mathlib
import Definitions.Def_ChapterWaveUnboundedPotential
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterStrichartzWave
import Definitions.Def_ChapterWaveBoundedPotential
open BookProof.StrichartzWave



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace ENNReal

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]

variable {ι : Type*} [Fintype ι]
Formal statement
theorem BookProof.StrichartzWave.wave_add_boundedPotentialOp_essentiallySelfAdjoint (n : ℕ) (W : SpaceTime n → ℝ)
    (hW : Function.HasTemperateGrowth W)
    (hmem : MemLp (fun x => (W x : ℂ)) (⊤ : ℝ≥0∞) (volume : Measure (SpaceTime n))) :
    BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain (SpaceTime n))
      (opL2 (waveOp n 0 + potentialOp W)) := by sorry

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