Prove2Me

`BookProof.StrichartzWave.wave_add_boundedPotential_essentiallySelfAdjoint` (n : ℕ) (W : Lp ℂ (⊤ : ℝ≥0∞) (volume : Measure (SpaceTime n))) (hW : ∀ᵐ x ∂(volume : Measure (SpaceTime

Proved
BookProof.StrichartzWave.wave_add_boundedPotential_essentiallySelfAdjoint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWaveBoundedPotential.

BookProof.StrichartzWave.wave_add_boundedPotential_essentiallySelfAdjoint (n : ℕ) (W : Lp ℂ (⊤ : ℝ≥0∞) (volume : Measure (SpaceTime n))) (hW : ∀ᵐ x ∂(volume : Measure (SpaceTime n)), (starRingEnd ℂ) (W x) = W x) : BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain (SpaceTime n)) (opL2 (waveOp n 0) + ((mulL2 W).toLinearMap ∘ₗ (schwartzDomain (SpaceTime n)).subtype))

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

Preamble
-- Generated from ChapterWaveBoundedPotential.lean — theorem BookProof.StrichartzWave.wave_add_boundedPotential_essentiallySelfAdjoint
import Mathlib
import Definitions.Def_ChapterWaveBoundedPotential
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterStrichartzWave
open BookProof.StrichartzWave



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace ENNReal

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]
Formal statement
theorem BookProof.StrichartzWave.wave_add_boundedPotential_essentiallySelfAdjoint (n : ℕ)
    (W : Lp ℂ (⊤ : ℝ≥0∞) (volume : Measure (SpaceTime n)))
    (hW : ∀ᵐ x ∂(volume : Measure (SpaceTime n)), (starRingEnd ℂ) (W x) = W x) :
    BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain (SpaceTime n))
      (opL2 (waveOp n 0) +
        ((mulL2 W).toLinearMap ∘ₗ (schwartzDomain (SpaceTime n)).subtype)) := by sorry

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