Prove2Me

`BookProof.FourierMultiplierEsa.firstOrderOp_essentiallySelfAdjoint` (c : ι → ℝ) (w : ι → V) : BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain V) (opL2 (firstOrderOp

Proved
BookProof.FourierMultiplierEsa.firstOrderOp_essentiallySelfAdjoint

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFourierMultiplierEsa.

BookProof.FourierMultiplierEsa.firstOrderOp_essentiallySelfAdjoint (c : ι → ℝ) (w : ι → V) : BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain V) (opL2 (firstOrderOp c w))

Formalization note: Lean 4 identifier BookProof.FourierMultiplierEsa.firstOrderOp_essentiallySelfAdjoint.

Preamble
-- Generated from ChapterFourierMultiplierEsa.lean — theorem BookProof.FourierMultiplierEsa.firstOrderOp_essentiallySelfAdjoint
import Mathlib
import Definitions.Def_ChapterFourierMultiplierEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterStrichartzWave
open BookProof.StrichartzWave
open BookProof.FourierMultiplierEsa



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace LineDeriv
open BookProof.StrichartzWave

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]
variable {ι : Type*} [Fintype ι]
Formal statement
theorem BookProof.FourierMultiplierEsa.firstOrderOp_essentiallySelfAdjoint (c : ι → ℝ) (w : ι → V) :
    BookProof.FarisLavine.EssentiallySelfAdjointOn (schwartzDomain V)
      (opL2 (firstOrderOp c w)) := by sorry

View graph