Prove2Me

`BookProof.StrichartzWave.multiplierOp_apply_eq` (m : V β†’ ℝ) (f : 𝓒(V, β„‚)) : (multiplierOp m f : 𝓒(V, β„‚)) = 𝓕⁻ (potentialOp m (𝓕 f : 𝓒(V, β„‚)))

Proved
BookProof.StrichartzWave.multiplierOp_apply_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWaveUnboundedPotential.

BookProof.StrichartzWave.multiplierOp_apply_eq (m : V β†’ ℝ) (f : 𝓒(V, β„‚)) : (multiplierOp m f : 𝓒(V, β„‚)) = 𝓕⁻ (potentialOp m (𝓕 f : 𝓒(V, β„‚)))

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

Preamble
-- Generated from ChapterWaveUnboundedPotential.lean β€” theorem BookProof.StrichartzWave.multiplierOp_apply_eq
import Mathlib
import Definitions.Def_ChapterWaveUnboundedPotential
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.multiplierOp_apply_eq (m : V β†’ ℝ) (f : 𝓒(V, β„‚)) :
    (multiplierOp m f : 𝓒(V, β„‚)) = 𝓕⁻ (potentialOp m (𝓕 f : 𝓒(V, β„‚))) := by sorry

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