`BookProof.FourierMultiplierEsa.fourier_mixedOp_apply` (a c : ι → ℝ) (w : ι → V) (κ : ℝ) (f : 𝓢(V, ℂ)) (x : V) : (𝓕 (mixedOp a c w κ f) : 𝓢(V, ℂ)) x = ((mixedSymbolFn a c...
ProvedBookProof.FourierMultiplierEsa.fourier_mixedOp_applytheoremstimepiece
Prove the following Lean 4 theorem from ChapterFourierMultiplierEsa.
BookProof.FourierMultiplierEsa.fourier_mixedOp_apply (a c : ι → ℝ) (w : ι → V) (κ : ℝ) (f : 𝓢(V, ℂ)) (x : V) : (𝓕 (mixedOp a c w κ f) : 𝓢(V, ℂ)) x = ((mixedSymbolFn a c w κ x : ℝ) : ℂ) * (𝓕 f : 𝓢(V, ℂ)) x
Formalization note: Lean 4 identifier BookProof.FourierMultiplierEsa.fourier_mixedOp_apply.
Preamble
-- Generated from ChapterFourierMultiplierEsa.lean — theorem BookProof.FourierMultiplierEsa.fourier_mixedOp_apply
import Mathlib
import Definitions.Def_ChapterFourierMultiplierEsa
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.fourier_mixedOp_apply (a c : ι → ℝ) (w : ι → V) (κ : ℝ) (f : 𝓢(V, ℂ)) (x : V) :
(𝓕 (mixedOp a c w κ f) : 𝓢(V, ℂ)) x
= ((mixedSymbolFn a c w κ x : ℝ) : ℂ) * (𝓕 f : 𝓢(V, ℂ)) x := by sorry